When I launch Minecraft Forge + Project: RED + CodeChickenLib version 1.0.0.61 installed, the game crashes on launch with an error stating that:

Forge Mod Loader has found a problem with your minecraft installation
The mods and versions listed below could not be found
CodeChickenCore : Any
The file 'ForgeModLoader-client-0.log' contains more information

I can upload the ForgeModLoader-client-0.log file if you want. The particular line:

014-04-08 13:22:33 [SEVERE] [ForgeModLoader] The mod ProjRed|Core (ProjectRed) requires mods [CodeChickenCore] to be available

May contain useful information.

The error literally states what's wrong, you need CodeChickenCore which is not the same as CodeChickenLib.
Specifically, you should have CodeChickenCore 0.9.0.9 and CodeChickenLib 1.0.0.61

Uhhhhhhh? THAT'S NOT INTUITIVE! I thought they were THE SAME FREAKING THING!!! sighs I am an idiot...

AND IT'S STILL CRASHING. GREAT. Different error though:
---- Minecraft Crash Report ----
// Ooh. Shiny.

Time: 4/8/14 2:05 PM
Description: There was a severe problem during mod loading that has caused the game to fail

cpw.mods.fml.common.LoaderException: java.lang.NoClassDefFoundError: mrtjp/projectred/transmission/PowerWire_100v
at cpw.mods.fml.common.LoadController.transition(LoadController.java:156)
at cpw.mods.fml.common.Loader.loadMods(Loader.java:523)
at cpw.mods.fml.client.FMLClientHandler.beginMinecraftLoading(FMLClientHandler.java:183)
at net.minecraft.client.Minecraft.func_71384_a(Minecraft.java:473)
at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:808)
at net.minecraft.client.main.Main.main(SourceFile:101)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
at java.lang.reflect.Method.invoke(Method.java:597)
at net.minecraft.launchwrapper.Launch.launch(Launch.java:131)
at net.minecraft.launchwrapper.Launch.main(Launch.java:27)
Caused by: java.lang.NoClassDefFoundError: mrtjp/projectred/transmission/PowerWire_100v
at mrtjp.projectred.ProjectRedExpansion$.preInit(ProjectRedExpansion.scala:27)
at mrtjp.projectred.ProjectRedExpansion.preInit(ProjectRedExpansion.scala)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
at java.lang.reflect.Method.invoke(Method.java:597)
at cpw.mods.fml.common.FMLModContainer.handleModStateEvent(FMLModContainer.java:545)
at sun.reflect.GeneratedMethodAccessor4.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
at java.lang.reflect.Method.invoke(Method.java:597)
at com.google.common.eventbus.EventHandler.handleEvent(EventHandler.java:74)
at com.google.common.eventbus.SynchronizedEventHandler.handleEvent(SynchronizedEventHandler.java:45)
at com.google.common.eventbus.EventBus.dispatch(EventBus.java:313)
at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:296)
at com.google.common.eventbus.EventBus.post(EventBus.java:267)
at cpw.mods.fml.common.LoadController.sendEventToModContainer(LoadController.java:201)
at cpw.mods.fml.common.LoadController.propogateStateMessage(LoadController.java:181)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
at java.lang.reflect.Method.invoke(Method.java:597)
at com.google.common.eventbus.EventHandler.handleEvent(EventHandler.java:74)
at com.google.common.eventbus.SynchronizedEventHandler.handleEvent(SynchronizedEventHandler.java:45)
at com.google.common.eventbus.EventBus.dispatch(EventBus.java:313)
at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:296)
at com.google.common.eventbus.EventBus.post(EventBus.java:267)
at cpw.mods.fml.common.LoadController.distributeStateMessage(LoadController.java:112)
at cpw.mods.fml.common.Loader.loadMods(Loader.java:522)
... 10 more
Caused by: java.lang.ClassNotFoundException: mrtjp.projectred.transmission.PowerWire_100v
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:186)
at java.lang.ClassLoader.loadClass(ClassLoader.java:306)
at java.lang.ClassLoader.loadClass(ClassLoader.java:247)
... 38 more
Caused by: java.lang.NoClassDefFoundError: mrtjp/projectred/transmission/PowerWire
at java.lang.ClassLoader.defineClass1(Native Method)
at java.lang.ClassLoader.defineClassCond(ClassLoader.java:637)
at java.lang.ClassLoader.defineClass(ClassLoader.java:621)
at java.security.SecureClassLoader.defineClass(SecureClassLoader.java:141)
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:178)
... 40 more
Caused by: java.lang.ClassNotFoundException: mrtjp.projectred.transmission.PowerWire
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:97)
at java.lang.ClassLoader.loadClass(ClassLoader.java:306)
at java.lang.ClassLoader.loadClass(ClassLoader.java:247)
... 45 more

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

-- System Details --
Details:
Minecraft Version: 1.6.4
Operating System: Mac OS X (x86_64) version 10.9.2
Java Version: 1.6.0_65, Apple Inc.
Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Apple Inc.
Memory: 31785576 bytes (30 MB) / 130060288 bytes (124 MB) up to 1065025536 bytes (1015 MB)
JVM Flags: 1 total; -Xmx1G
AABB Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used
Suspicious classes: FML and Forge are installed
IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0
FML: MCP v8.11 FML v6.4.45.953 Minecraft Forge 9.11.1.953 13 mods loaded, 13 mods active
mcp{8.09} [Minecraft Coder Pack] (minecraft.jar) Unloaded->Constructed->Pre-initialized
FML{6.4.45.953} [Forge Mod Loader] (minecraftforge-9.11.1.953.jar) Unloaded->Constructed->Pre-initialized
Forge{9.11.1.953} [Minecraft Forge] (minecraftforge-9.11.1.953.jar) Unloaded->Constructed->Pre-initialized
CodeChickenCore{0.9.0.9} [CodeChicken Core] (minecraft.jar) Unloaded->Constructed->Pre-initialized
ForgeMultipart{1.0.0.244} [Forge Multipart] (ForgeMultipart-universal-1.6.4-1.0.0.244.jar) Unloaded->Constructed->Pre-initialized
ProjRed|Core{4.3.5.30} [ProjectRed] (ProjectRedBase-1.6.4-4.3.5.30.jar) Unloaded->Constructed->Pre-initialized
ProjRed|Transportation{4.3.5.30} [ProjectRed-Transportation] (ProjectRedMechanical-BETA-1.6.4-4.3.5.30.jar) Unloaded->Constructed->Pre-initialized
ProjRed|Compatibility{4.3.5.30} [ProjectRed-Compatibility] (ProjectRedCompat-1.6.4-4.3.5.30.jar) Unloaded->Constructed->Pre-initialized
ProjRed|Integration{4.3.7.32} [ProjectRed-Integration] (ProjectRedIntegration-1.6.4-4.3.7.32.jar) Unloaded->Constructed->Errored
ProjRed|Transmission{4.3.7.32} [ProjectRed-Transmission] (ProjectRedIntegration-1.6.4-4.3.7.32.jar) Unloaded->Constructed->Errored
ProjRed|Expansion{4.3.5.30} [ProjectRed-Expansion] (ProjectRedMechanical-BETA-1.6.4-4.3.5.30.jar) Unloaded->Constructed->Errored
McMultipart{1.0.0.244} [Minecraft Multipart Plugin] (ForgeMultipart-universal-1.6.4-1.0.0.244.jar) Unloaded->Constructed->Pre-initialized
ForgeMicroblock{1.0.0.244} [Forge Microblocks] (ForgeMultipart-universal-1.6.4-1.0.0.244.jar) Unloaded->Constructed->Pre-initialized

You have 2 versions of ProjectRed at the same time, a big no no.
Update Core,Transportation, Compatibility and Expansion to 4.3.7.32
Your Integration and Transmission modules are already up to date.