To start this quest you should try to open Well-Worn Chest (lvl 10) located in the Captain's Cabin on the second floor of The Black Bull tavern.
We came across a locked chest that spoke to us, demanding the password. Such sophisticated precautions must surely hide a rich bounty...

1. Talked Adventurer Sleep
Talk to A Dozing Adventurer sleeping on a nearby bed and tell him you are his mother. Suddenly awakened, he will give you a password.
In a guest room upstairs at the Black Bull tavern, we encountered a man who is mumbling to himself in his sleep.

2. Open Adventurer Chest
Talk to the chest again, password is "the word".
We managed to open the talking chest.
3. Destroy Adventurer Chest
You can also destroy the chest.

4. Close Left RC
We have left Reaper's Coast. It seems we'll never find out what was inside that chest.