You said you put a new chain on it, didn't you? Did you size the chain to the old chain? Chains are sold longer than what most bike need. Too long a chain can mean the rear derailleur can't keep enough tension on it and falling off the front chain ring can be a result sometimes.

If your bike isn't high mileage with 20,000 miles on it, then I'd think it unlikely your chain ring worn out. There is a lot of shaping and sculpting of the chain ring teeth to help it shift better in the front and some teeth can look worn out if you aren't comparing to a new ring of the same model.

Still....................what bike do you have? If you only have a criterium bike, then we can eliminate quite a few potential solutions.