I've been told that you can get an oval stone from a captured Chansey, but I cannot find where to catch one. Where can I find an oval stone?
you can obtain a Oval stone in the left part of the Unknown Dungeon.
After becoming the Pokemon League Champion, the Unknown Dungeon at the northern part of Pokemon Village will become accessible. Since you can't Fly to Pokemon Village, you'll have to make your way through the Winding Woods again. The quick path is south, west, northwest, southwest, south, and south through Route 20.
You can't get the oval stone from wild Pokémon, but there is one hidden in a rock in the Unknown Dungeon of Pokémon Village. This video shows you where to get it.
You can catch Chansey in the friend safari. However, a wild Chansey might hold a lucky punch or a lucky egg, but not an oval stone. While Happiny is coded to be able to hold an oval stone in the wild, you can only get a Happiny in X and Y by breeding Chansey.