Locked chests appear all over Tartarus in Persona 3 Reload, and they'll require Twilight Fragments to open. The location of locked chests on the regular floors of Tartarus will disappear when you leave, but the chests on floors with the Gatekeeper Shadows are permanent. The treasures on Gatekeeper Floors usually contain exclusive armor and weapons. You will need to unlock one of these Gatekeeper Floor-chests to get the Ote-gine Spear, which is used for completing one of Elizabeth's Requests in Persona 3 Reload.