Interestingly, despite being able to hold a block in my hand and see its physical form in my hand, placing one causes my game to crash. Fiddled around with a couple different versions and it only got worse or had no effect. Here is the crash report:

---- Minecraft Crash Report ----

WARNING: coremods are present:
CCLCorePlugin (CodeChickenLib-1.10.2-2.5.9.283-universal.jar)
CTMCorePlugin (CTM-MC1.10.2-0.2.2.24.jar)
NEICorePlugin (NotEnoughItems-1.10.2-2.1.3.220-universal.jar)
AppleCore (AppleCore-mc1.10.2-2.2.2.jar)
Contact their authors BEFORE contacting forge

// Daisy, daisy...

Time: 9/3/17 9:00 PM
Description: Tesselating block model

com.google.common.util.concurrent.ExecutionError: java.lang.NoSuchMethodError: team.chisel.ctm.api.util.RenderContextList.getRenderContext(Lteam/chisel/ctm/api/texture/ITextureType;)Lteam/chisel/ctm/api/texture/ITextureContext;
at com.google.common.cache.LocalCache$Segment.get(LocalCache.java:2199)
at com.google.common.cache.LocalCache.get(LocalCache.java:3934)
at com.google.common.cache.LocalCache$LocalManualCache.get(LocalCache.java:4736)
at team.chisel.ctm.client.model.AbstractCTMBakedModel.func_188616_a(AbstractCTMBakedModel.java:212)
at net.minecraftforge.client.model.pipeline.ForgeBlockModelRenderer.render(ForgeBlockModelRenderer.java:117)
at net.minecraftforge.client.model.pipeline.ForgeBlockModelRenderer.func_187498_b(ForgeBlockModelRenderer.java:103)
at net.minecraft.client.renderer.BlockModelRenderer.func_187493_a(BlockModelRenderer.java:46)
at net.minecraft.client.renderer.BlockModelRenderer.func_178267_a(BlockModelRenderer.java:37)
at net.minecraft.client.renderer.BlockRendererDispatcher.func_175018_a(BlockRendererDispatcher.java:81)
at codechicken.lib.render.block.CCExtendedBlockRendererDispatcher.func_175018_a(CCExtendedBlockRendererDispatcher.java:54)
at net.minecraft.client.renderer.chunk.RenderChunk.func_178581_b(RenderChunk.java:199)
at net.minecraft.client.renderer.chunk.ChunkRenderWorker.func_178474_a(SourceFile:100)
at net.minecraft.client.renderer.chunk.ChunkRenderDispatcher.func_178505_b(ChunkRenderDispatcher.java:171)
at net.minecraft.client.renderer.RenderGlobal.func_174970_a(RenderGlobal.java:952)
at net.minecraft.client.renderer.EntityRenderer.func_175068_a(EntityRenderer.java:1286)
at net.minecraft.client.renderer.EntityRenderer.func_78471_a(EntityRenderer.java:1229)
at net.minecraft.client.renderer.EntityRenderer.func_181560_a(EntityRenderer.java:1038)
at net.minecraft.client.Minecraft.func_71411_J(Minecraft.java:1076)
at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:371)
at net.minecraft.client.main.Main.main(SourceFile:124)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:498)
at net.minecraft.launchwrapper.Launch.launch(Launch.java:135)
at net.minecraft.launchwrapper.Launch.main(Launch.java:28)
Caused by: java.lang.NoSuchMethodError: team.chisel.ctm.api.util.RenderContextList.getRenderContext(Lteam/chisel/ctm/api/texture/ITextureType;)Lteam/chisel/ctm/api/texture/ITextureContext;
at team.chisel.client.render.ModelChiselBlock.addAllQuads(ModelChiselBlock.java:98)
at team.chisel.client.render.ModelChiselBlock.createModel(ModelChiselBlock.java:83)
at team.chisel.ctm.client.model.AbstractCTMBakedModel.lambda$getQuads$1(AbstractCTMBakedModel.java:212)
at com.google.common.cache.LocalCache$LocalManualCache$1.load(LocalCache.java:4739)
at com.google.common.cache.LocalCache$LoadingValueReference.loadFuture(LocalCache.java:3524)
at com.google.common.cache.LocalCache$Segment.loadSync(LocalCache.java:2317)
at com.google.common.cache.LocalCache$Segment.lockedGetOrLoad(LocalCache.java:2280)
at com.google.common.cache.LocalCache$Segment.get(LocalCache.java:2195)
... 25 more

A detailed walkthrough of the error, its code path and all known details is as follows:

-- Head --
Thread: Client thread
Stacktrace:
at com.google.common.cache.LocalCache$Segment.get(LocalCache.java:2199)
at com.google.common.cache.LocalCache.get(LocalCache.java:3934)
at com.google.common.cache.LocalCache$LocalManualCache.get(LocalCache.java:4736)
at team.chisel.ctm.client.model.AbstractCTMBakedModel.func_188616_a(AbstractCTMBakedModel.java:212)
at net.minecraftforge.client.model.pipeline.ForgeBlockModelRenderer.render(ForgeBlockModelRenderer.java:117)
at net.minecraftforge.client.model.pipeline.ForgeBlockModelRenderer.func_187498_b(ForgeBlockModelRenderer.java:103)

-- Block model being tesselated --
Details:
Block: chisel:glassdyedgray[variation=0]
Block location: World: (-53,4,-390), Chunk: (at 11,0,10 in -4,-25; contains blocks -64,0,-400 to -49,255,-385), Region: (-1,-1; contains chunks -32,-32 to -1,-1, blocks -512,0,-512 to -1,255,-1)
Using AO: true
Stacktrace:
at net.minecraft.client.renderer.BlockModelRenderer.func_187493_a(BlockModelRenderer.java:46)
at net.minecraft.client.renderer.BlockModelRenderer.func_178267_a(BlockModelRenderer.java:37)

-- Block being tesselated --
Details:
Block type: ID #639 (tile.chisel.glassdyedgray // null)
Block data value: 0 / 0x0 / 0b0000
Block location: World: (-53,4,-390), Chunk: (at 11,0,10 in -4,-25; contains blocks -64,0,-400 to -49,255,-385), Region: (-1,-1; contains chunks -32,-32 to -1,-1, blocks -512,0,-512 to -1,255,-1)
Stacktrace:
at net.minecraft.client.renderer.BlockRendererDispatcher.func_175018_a(BlockRendererDispatcher.java:81)

-- Block being tesselated --
Details:
Block type: ID #639 (tile.chisel.glassdyedgray // null)
Block data value: 0 / 0x0 / 0b0000
Block location: World: (-53,4,-390), Chunk: (at 11,0,10 in -4,-25; contains blocks -64,0,-400 to -49,255,-385), Region: (-1,-1; contains chunks -32,-32 to -1,-1, blocks -512,0,-512 to -1,255,-1)
Stacktrace:
at codechicken.lib.render.block.CCExtendedBlockRendererDispatcher.func_175018_a(CCExtendedBlockRendererDispatcher.java:54)
at net.minecraft.client.renderer.chunk.RenderChunk.func_178581_b(RenderChunk.java:199)
at net.minecraft.client.renderer.chunk.ChunkRenderWorker.func_178474_a(SourceFile:100)
at net.minecraft.client.renderer.chunk.ChunkRenderDispatcher.func_178505_b(ChunkRenderDispatcher.java:171)
at net.minecraft.client.renderer.RenderGlobal.func_174970_a(RenderGlobal.java:952)
at net.minecraft.client.renderer.EntityRenderer.func_175068_a(EntityRenderer.java:1286)
at net.minecraft.client.renderer.EntityRenderer.func_78471_a(EntityRenderer.java:1229)

-- Affected level --
Details:
Level name: MpServer
All players: 1 total; [EntityPlayerSP['ADventuresVDO'/49, l='MpServer', x=-52.91, y=4.00, z=-391.58]]
Chunk stats: MultiplayerChunkCache: 579, 579
Level seed: 0
Level generator: ID 01 - flat, ver 0. Features enabled: false
Level generator options:
Level spawn location: World: (-48,4,-385), Chunk: (at 0,0,15 in -3,-25; contains blocks -48,0,-400 to -33,255,-385), Region: (-1,-1; contains chunks -32,-32 to -1,-1, blocks -512,0,-512 to -1,255,-1)
Level time: 1078 game time, 1078 day time
Level dimension: 0
Level storage version: 0x00000 - Unknown?
Level weather: Rain time: 0 (now: false), thunder time: 0 (now: false)
Level game mode: Game mode: creative (ID 1). Hardcore: false. Cheats: false
Forced entities: 23 total; [EntitySheep['Sheep'/32, l='MpServer', x=-0.79, y=4.00, z=-434.30], EntitySheep['Sheep'/33, l='MpServer', x=-8.39, y=4.00, z=-429.20], EntitySheep['Sheep'/34, l='MpServer', x=-7.50, y=4.00, z=-427.50], EntityCow['Cow'/35, l='MpServer', x=-15.48, y=4.00, z=-331.20], EntityPlayerSP['ADventuresVDO'/49, l='MpServer', x=-52.91, y=4.00, z=-391.58], EntityCow['Cow'/36, l='MpServer', x=-8.78, y=4.00, z=-329.15], EntityLatchedRenderer['unknown'/3781, l='MpServer', x=8.50, y=65.00, z=8.50], EntitySheep['Sheep'/37, l='MpServer', x=9.73, y=4.00, z=-452.82], EntitySheep['Sheep'/38, l='MpServer', x=15.50, y=4.00, z=-461.50], EntityCow['Cow'/40, l='MpServer', x=9.50, y=4.00, z=-318.50], EntityCow['Cow'/41, l='MpServer', x=8.50, y=4.00, z=-317.50], EntityPig['Pig'/42, l='MpServer', x=9.50, y=4.00, z=-314.50], EntitySheep['Sheep'/43, l='MpServer', x=20.50, y=4.00, z=-466.50], EntityChicken['Chicken'/44, l='MpServer', x=22.28, y=4.00, z=-457.36], EntityPig['Pig'/18, l='MpServer', x=-33.25, y=4.00, z=-400.38], EntityCow['Cow'/20, l='MpServer', x=-22.43, y=4.00, z=-467.76], EntityPig['Pig'/23, l='MpServer', x=-22.50, y=4.00, z=-388.50], EntityPig['Pig'/24, l='MpServer', x=-22.50, y=4.00, z=-390.50], EntityLatchedRenderer['unknown'/15928, l='MpServer', x=-52.91, y=4.00, z=-391.58], EntityPig['Pig'/25, l='MpServer', x=-18.78, y=4.00, z=-392.45], EntityCow['Cow'/26, l='MpServer', x=-20.50, y=4.00, z=-324.50], EntityChicken['Chicken'/27, l='MpServer', x=-21.50, y=4.00, z=-328.50], EntitySheep['Sheep'/31, l='MpServer', x=-12.18, y=4.00, z=-427.78]]
Retry entities: 1 total; [EntityLatchedRenderer['unknown'/3781, l='MpServer', x=8.50, y=65.00, z=8.50]]
Server brand: fml,forge
Server type: Integrated singleplayer server
Stacktrace:
at net.minecraft.client.multiplayer.WorldClient.func_72914_a(WorldClient.java:415)
at net.minecraft.client.Minecraft.func_71396_d(Minecraft.java:2660)
at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:392)
at net.minecraft.client.main.Main.main(SourceFile:124)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:498)
at net.minecraft.launchwrapper.Launch.launch(Launch.java:135)
at net.minecraft.launchwrapper.Launch.main(Launch.java:28)

-- System Details --
Details:
Minecraft Version: 1.10.2
Operating System: Windows 7 (amd64) version 6.1
Java Version: 1.8.0_91, Oracle Corporation
Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation
Memory: 330966960 bytes (315 MB) / 1060372480 bytes (1011 MB) up to 1060372480 bytes (1011 MB)
JVM Flags: 6 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx1G -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M
IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0
FML: MCP 9.32 Powered by Forge 12.18.3.2185 23 mods loaded, 23 mods active
States: 'U' = Unloaded 'L' = Loaded 'C' = Constructed 'H' = Pre-initialized 'I' = Initialized 'J' = Post-initialized 'A' = Available 'D' = Disabled 'E' = Errored
UCHIJAAAA mcp{9.19} [Minecraft Coder Pack] (minecraft.jar)
UCHIJAAAA FML{8.0.99.99} [Forge Mod Loader] (forge-1.10.2-12.18.3.2185.jar)
UCHIJAAAA Forge{12.18.3.2185} [Minecraft Forge] (forge-1.10.2-12.18.3.2185.jar)
UCHIJAAAA NotEnoughItems{2.1.3.220} [Not Enough Items] (NotEnoughItems-1.10.2-2.1.3.220-universal.jar)
UCHIJAAAA ccl-entityhook{1.0} [ccl-entityhook] (CodeChickenLib-1.10.2-2.5.9.283-universal.jar)
UCHIJAAAA mercurius_updater{1.0} [mercurius_updater] (MercuriusUpdater-1.10.2.jar)
UCHIJAAAA JEI{3.14.7.420} [Just Enough Items] (jei_1.10.2-3.14.7.420.jar)
UCHIJAAAA AppleCore{2.2.2} [AppleCore] (AppleCore-mc1.10.2-2.2.2.jar)
UCHIJAAAA BiblioCraft{2.2.5} [BiblioCraft] (BiblioCraft[v2.2.5][MC1.10.2].jar)
UCHIJAAAA cfm{4.1.2} [MrCrayfish's Furniture Mod] (cfm-4.1.2-mc1.10.2.jar)
UCHIJAAAA chisel{MC1.10.2-0.0.13.29} [Chisel] (Chisel-MC1.10.2-0.0.13.29.jar)
UCHIJAAAA CodeChickenLib{2.5.9.283} [CodeChicken Lib] (CodeChickenLib-1.10.2-2.5.9.283-universal.jar)
UCHIJAAAA CodeChickenCore{2.4.1.102} [CodeChicken Core] (CodeChickenCore-1.10.2-2.4.1.102-universal.jar)
UCHIJAAAA ctm{MC1.10.2-0.2.2.24} [CTM] (CTM-MC1.10.2-0.2.2.24.jar)
UCHIJAAAA extrautils2{1.0} [Extra Utilities 2] (extrautils2-1.10.2-1.6.jar)
UCHIJAAAA ichunutil{6.3.2} [iChunUtil] (iChunUtil-1.10.2-6.3.2.jar)
UCHIJAAAA musiccraft{3.0.1} [MusicCraft] (musiccraft-3.0.1.jar)
UCHIJAAAA harvestcraft{1.10.2j} [Pam's HarvestCraft] (Pam's HarvestCraft 1.10.2j.jar)
UCHIJAAAA personalcars{1.0} [Personal Cars] (Personal-Cars-Mod-1.10.2.jar)
UCHIJAAAA portalgun{6.0.1} [PortalGun] (PortalGun-1.10.2-6.0.1.jar)
UCHIJAAAA SpiceOfLife{1.3.8} [The Spice of Life] (SpiceOfLife-mc1.9.4-1.3.8.jar)
UCHIJAAAA bspkrsCore{at_0.9} [bspkrsCore] (Treecapitator-1.10.2-at_0.9.jar)
UCHIJAAAA Treecapitator{at_0.9} [Treecapitator] (Treecapitator-1.10.2-at_0.9.jar)
Loaded coremods (and transformers):
CCLCorePlugin (CodeChickenLib-1.10.2-2.5.9.283-universal.jar)
codechicken.lib.asm.ClassHeirachyManager
codechicken.lib.asm.CCL_ASMTransformer
CTMCorePlugin (CTM-MC1.10.2-0.2.2.24.jar)
team.chisel.ctm.client.asm.CTMTransformer
NEICorePlugin (NotEnoughItems-1.10.2-2.1.3.220-universal.jar)
codechicken.nei.asm.NEITransformer
AppleCore (AppleCore-mc1.10.2-2.2.2.jar)
squeek.applecore.asm.TransformerModuleHandler
GL info: ' Vendor: 'NVIDIA Corporation' Version: '4.5.0 NVIDIA 347.88' Renderer: 'GeForce GTX 750/PCIe/SSE2'
NotEnoughItems Invalid Fingerprint Reports:
CodeChickenLib Invalid Fingerprint Reports:
CodeChickenCore Invalid Fingerprint Reports:
Launched Version: 1.10.2-forge1.10.2-12.18.3.2185
LWJGL: 2.9.4
OpenGL: GeForce GTX 750/PCIe/SSE2 GL version 4.5.0 NVIDIA 347.88, NVIDIA Corporation
GL Caps: Using GL 1.3 multitexturing.
Using GL 1.3 texture combiners.
Using framebuffer objects because OpenGL 3.0 is supported and separate blending is supported.
Shaders are available because OpenGL 2.1 is supported.
VBOs are available because OpenGL 1.5 is supported.

Using VBOs: Yes
Is Modded: Definitely; Client brand changed to 'fml,forge'
Type: Client (map_client.txt)
Resource Packs: 
Current Language: English (US)
Profiler Position: N/A (disabled)
CPU: 6x AMD FX(tm)-6300 Six-Core Processor 

Your Chisel version is outdated.