BioShock

To open the chest, you must kill Cohen, and you will find the Muse Key on his person. When you have that you can open the chest.
Though I strongly suggest that you do not kill him yet!! Instead, wait till you get to the Olympus Heights level, and you will find his apartment somewhere in that level, kill the dancing splicers in the apartment, and Cohen will come down from his room, and then kill him and take the key. After that go up to his room and you will find a Power To The People station. (see, if you kill him in Fort Frolic, you won't be able to enter his room, therefore disabling you from getting all weapon upgrades)

The reward is rather disappointing. all you will find in the chest is $100, 8 Incendiary Bolts, and 3 Spider Splicer Organs.

You need the Muse Key from his corpse. At Olympus Heights at his apartment you'll see a door on the right and two dancing splicers straight ahead. Stand next to the door and shoot a trap arrow at the frame to the left and duck. Shoot another arrow and strafe left so out of way. Stand and repeat. You should have 4 trap arrow lines in front of the door. Shoot a frag grenade at the dancers feet to kill them and with luck Cohen will run out the door and into all 4 lines killing him without any trouble. Take his picture and search his corpse for the key. Go upstairs for the Weapon Upgrade and use the bathosphere to return to Fort Frolic to open the case. Like Godamit says it contains $100, 8 Incendiary Bolts and 3 organs.

Simple. Kill Cohen. HOWEVER!!!!! You do not want to kill him right now. Wait till you get into olympis heights. He will be there and then you want to kill him. That way you can get to the Power to the People machine and he'll be way easier. though the reward isn't great at all. It's like 100 dollars, ammo for a gun and nothing else really.

Simply put, the reward is not worht the trouble to pro gamers.