Discord just had an update to version 0.0.2; the version available in the repository is still at 0.0.1. Upon launching, it will prompt the user to download the latest update; ignoring this message and selecting "I'll figure it out" will cause Discord to quit.
@JoshStrobl said in IRC that the new version (0.0.2) in its current state is borked; it now requires LLVM libc++.