Running a 1/8 chain on 3/32 sprocket & chainring?

Bear in mind that the 'flexibility' of 3/32 chains designed for derailleur geared bikes may be a curse - they only stay on the rear sprocket of a multi-speed set-up with the help of the rear mech. If the chainline is not good, they may simply climb off the rear sprocket. I would go for a 3/32 chain designed for ss/fixed use and highly recommend the KMC-Z610HX - as good as most track chains (in fact the same apart from size as the Z510HX which is a very good 1/8" chain). Personally I would only resort to 1/8" if either the front or rear are also 1/8" (or both of course!). Oh, and sort your chainline out - if nothing else it will make it much better to ride ;-)

I meant singlespeed 3/32 chain TBH.

+1 on the sort your chainline out though.
Hub spacers, different bb spindle, chainring bolt spacers etc. etc.