What is causing the chain skip after chain replacement? I have a road bike that was converted to single speed with a single sprocket on the read wheel and a single chainring. 

I had a 3/32 chain which worked perfectly fine. However after many kms and apparent chains stretch I decided to replace the chain.

I replaced the chain with a single speed 1/8 chain which I assumed would work perfectly, given that there's a single sprocket and chain pitch is standard.


  All modern bicycle chains are made to the “one-half inch pitch” standard, meaning from rivet to rivet is nominally 0.5 inches. The sprocket teeth are cut for this same one-half inch standard to accept bicycle chains. However, this does not mean all makes and models of chains are interchangeable. source


Since I replaced the chain, the chain skips on the rear sprocket due to what appear to be misalignment which compounds after a couple of revolutions and then skips. 

I tried adjusting the chain tension but that doesn't seem to help.



Hypothesis to explain the problem:


The stretched chain had deviated from standard pitch and caused the sprocket (which is relatively old) to match it through constant wear. 


How reasonable is that? Should I just replace the sprocket? Could the problem be elsewhere?
Yes, the stretched chain wears the chain ring and sprockets to match its pitch. It's recommended to use a chain gauge (such as this one by Park Tools) so you can replace your chain before it's stretched enough to do significant damage to the rest of the drive train. If you do let the chain stretch too far, you'll need to change the cassette/rear cog and/or chain ring(s).

The teeth of new chain rings have a mostly symmetrical profile; worn ones acquire a characteristic "shark fin" shape that's steeper on one side than the other and quite pointy at the top. On a one-by or single-speed bike, that's pretty easy to identify; on a bike with front derailleurs, be aware that the chain rings tend to have several teeth with funny profiles from new, to aid with shifting.