A golden chest will appear when you defeat one (or both if there are more than one of them in a room) of the many mini-bosses you come across. The mini-bosses are easily identifiable as being MUCH larger versions of the regular enemies and hit much harder than their regular counterparts.
Here's a list of the enemies in the game and pictures associated with each enemy. Mini-bosses usually have a unique name, like Berith and Halphas instead of "Skeleton".
http://rogue-legacy.wikia.com/wiki/Enemies