"error: syntax error before '*' token"

I recently began porting Jumper to the iPhone as a winter project. After adding another source file (Level.c in this case), I started getting thousands of build errors, along the lines of:

error: syntax error before '@' token
error: syntax error before '*' token

These were from files in /Developer/Platforms/iPhoneSimulator.platform/..., which was not encouraging. Something weird was going on.

Actually, it was really simple. Turns out that should have been Level.m, not .c. Whoops.