Originally Posted by FBinNY

Your chain is too narrow for the gap between the rings. That allows the tips of the teeth to snag it between the plates, while it's supported by the inside face of the outer ring. If the gap were narrower, or more logically, the chain were wider it would push over and the teeth would drop into the chain.

FYI - 7/6s chains are made around the spacing of 7s and ultra 6s sprockets. For this older bike, you want a chain that says 6s or 6s/5s to get the added width needed.