The chain has to match your cogs and chain ring... 3/32 rings, cogs, and chains work just fine on a fixed gear.
I have a few bikes with mismatched cogs so run 1/8 chain or simply run the 1/8 because I got such a great deal on it... the wider chain does not cause problems on a 3/32 chain ring or cog and is marginally stronger.
People get really pissed (even the fg guys) when old and often valuable bikes get irrevocably altered when they get turned into fixed gear bikes... a good rule is not to do anything you can't undo.
On that note... what kind of bike is it ?