All across the dungeons on UO: Depths there will be two kinds of chests that you will be encountering.

One is the "Guarded Treasure Chest", to open this chest you must kill the guardian of the chest, which can be a Rotting Corpse or a Drake.
As a reward you'll find gold, magical items and can also find Treasure Maps, Artifacts obtainable normally only from BODs, or greater magical items, that can be specially hued.
This chest is orange.

The other kind of chest is a Locked Chest. It can be opened by the use of the skill Lockpicking and will require several Lockpicks, which can be lost on a failed attempt. These chests can come in several levels:

Level 0 - being openable by anyone, but giving lower rewards.
Level 1 - being openable by people with 20.0 or more Lockpicking.
Level 2 - being openable by people with 40.0 or more lockpicking.
Level 3 - being openable by people with 60.0 or more lockpicking.
Level 4 - being openable by people with 80.0 or more lockpicking.
Level 5 - being openable by people with 100.0 or more lockpicking
and Level 6 - being openable by people with 110.0 or more lockpicking.

Opening these chests are the only way to get a power scroll for Stealing, Lockpicking and Removetrap. As the level of the chest increases, so does the chance of finding one.
You can also get minor artifacts and Set Items.

The level of the chest are completely random, meaning that a chest that appeared in a place X, can be of level 0 to 6.

Chests can come as trapped to, so you must use the Removetrap skill to disarm it. A failed disarm will result in the trap getting activated.

Beware that once a chest is opened you have 60 seconds to get everything from it, or it'll disappear being replaced by another chest.