You have to put one of the items from the Peninsula tomb into the chest. You did go there, right?
Each of the tombs have a chest next to a door with a note that has a clue as to which of the ceremonial items go into the chest. So 'a splinter in flight' refers to the Ceremonial Arrow.
If you don't have the Ceremonial items, first finish the Beggar's Nest area then go back to the Peninsula tomb to get them, If you go earlier you'll have a longer journey.