converting to fixed gear, chain problem
You might have bought the wrong width chain. For road bikes/fixie there are two possibilities. These are the width of the chain. 
3/32" and 1/8"

a 3/32" chain will not fit on a 1/8" cog but a 1/8" chain will fit on a 3/32" cog (but with extra space around the teeth).



If it is the length of the chain you are talking about then get a new chain. but the pedal cog might also need to be replaced.

More economic route might be buying a used rear cog (be warned this might be unsafe if you end up riding a lot wear will be faster)