The Loric Chest that was given to Number Six traveled with her and Katarina once they had arrived on Earth.
After fleeing Mexico when Six replies to Two's blog post, and a run in with Mogadorians in Texas, Katarina accepts that the Mogadorians are on to them and decides to hide Six's Chest. They travel to Lake Ouachita in Arkansas, somewhere they had once camped, and Six buries in on an island in the middle of the lake.
Six and Katarina are later captured in New York but when Six finally escapes and travels back to the lake to collect her Chest, it has already been taken. Its current location is unknown, though the fact that it was not at the Mogadorian Mountain Base, along with Four and Nine's chest, suggests that it is not in the possession of the Mogadorians. Items in the chest are also unconfirmed as it was not opened before it disappeared.