Your 4 most recently won chests are stored in the 'Chest Drawer', which can be opened by tapping on the '<<' arrow on the far right side of the game window. 

To open a chest, the required time must elapse to unlock the chest. You can only have one chest unlocking at one time. 

You can also instantly open a chest by using gems. Each 10 minute time period costs 1 gem.

Free chests can be opened instantly when they're available. Purchased chests can also be opened instantly.