Chests are found throughout the game in dungeons. The current dungeons in the game are the Ancient Forest Temple dungeon and the Cave Descent dungeon. Chests are dropped by the bosses of those dungeons.
There are two types of chests, one requires that you buy a key for 15 Robux or buying the Infinity Key gamepass to unlock all further chests for the price of 450 Robux. This chest can be recognised by the larger scale than the normal one and the violet particles.
The normal chest however doesn't urge you to buy anything to open them, instead you get items off them by sheer luck.