Location 1: Claptrap
There are two chests in close proximity of a damaged claptrap. The first is right next to him. The second one will be revealed upon fixing the aforementioned claptrap. Follow him.
Location 2: Second Respawn
Pass a large elevator, there will be an arrow pointing to the right. Instead of going right, go left and enter a giant room where there are two chests, an ammo chest and one red chest.
Location 3: Jumping Time
After leaving the second respawn point at the top of the elevator, go through the door that hasn't been entered yet and immediately turn left. Go up the stairs and at the top turn right. There should be a platform. Jump onto the platform and the chest should be within viewing distance. Face east.
- It is not recommended to farm the area until the Roid Rage Psycho has been killed and the mine key taken. This will open a shortcut between the first hallway and the circular room where 4 midgets will run an ambush. (on the map it's first turn right). Using this shortcut will prevent enemies from spawning in the area where the injured Claptrap was, allowing easy access to the chests there. The circular area with four Midgets itself also can be skipped by simply running through it. This leaves only the enemies in the first corridor to deal with. A Siren can just Phasewalk through them.
- Do not forget to check the two lockers in the room opened after Claptrap is fixed. They're set to always spawn items so it's possible to get Revolvers, repeaters, grenade mods or shields from them.