To set a custom resolution go to \SteamApps\common\Antichamber\UDKGame\Config and open DefaultEngine.ini (Notepad will work just fine). Find (Ctrl + F on Notepad) [SystemSettings], change both ResX and ResY to your desired resolution, save the file and you're good to go.

Example:

[SystemSettings]
UseVsync=True
CompositeDynamicLights=False
ResX=1360
ResY=768
Fullscreen=True

Note: The in-game menu won't show your current resolution, changing it there will probably undo your manual changes.