well here is the word from Sheldon Brown

1/8" or 3/32" Chain?

Many track bicycles use a wider chain than is common on multi-speed bicycles. Derailer-type chain has a nominal internal width of 3/32". Single-speed bicycles, including most track bicycles, use the wider 1/8" size. You can buy fixed-gear sprockets in both sizes.

(Some people mistakenly refer to the width as "pitch", speaking of "road pitch" or "track pitch". This is a malapropism. The pitch is the distance between the rollers, and all modern bicycle chain has the same pitch, 1/2"/12.7 mm.)

I would generally advise using the 3/32" (derailer) size. It is lighter, more compatible with your existing chainwheels, and likely to run smoother if the chainline is less than perfect, due to beveled side plates. In my experience, 3/32" chain is no less durable or reliable than 1/8".
For the true retro fan, another option is 1" x 3/16" chain. This used to be common on track bikes. This requires special sprockets with only half as many teeth as standard 1/2" pitch sprockets. Serious old-time trackies used "block" chain, which had no rollers. This is no longer available. Roller chain is still sometimes findable in this size.

Even more obscure is the 10 mm pitch chain promoted by Shimano a few years back. The idea was to save weight by making everything littler. An idea whose time never came.