You can protect chests, doors, and individual blocks with sign protection. If you need to protect your base, you should be using chunk claiming instead, however.
There are two ways to lock a block:
To make a "lock sign," just place a regular sign (either standing or a wall one) and place:
Because you can't place a sign onto a chest (and some other types of blocks), you can sneak (default key SHIFT) and then right click the chest.