My bet is that you have a worn cassette. That's common when replacing a well worn chain. Try shifting into the rear cog that you use the least often and see if that one happens to run a little smoother.
When a chain wears, it sctually stretches and changes pitch by a small amount. When that happens gradually, it also wears the cassette cogs to match the new pitch. Now, when you replace the chain, the cassette is the wrong pitch to match the new chain and the chain kind of skips over the tops of the cogs.