When I put my Gitane back together with a new chain it skipped in fourth but not fifth. This was with a brand new chain. I switched freewheels with a known good one and it still skipped, just a little less. After a 14 mile ride it doesn't skip at all now.

I put the skipping freewheel on another bike and it doesn't skip. Maybe the chain is worn a bit? In this case maybe a little chain wear is a good thing.

My chrome Paramount is going to start getting some attention this morning. I can't wait to try it out!