Close. There's a save point at the base of the stairs just after facing Proud Clod. You can change your party there to put Barret in if you don't normally use him. Just put him in your party, run up the stairs and open the chest. The you can return to the save point and change your party if you so wish.Originally Posted by medigodoom
Another hint for that area: pick up the Mystile from the chest on the right-hand side just after the PC battle. You can also steal Shinra Alphas from the SOLDIER:1st if you missed them in the Underwater Reactor.