Finding the Garden of Eden

 is a Fallout 3 quest. It is also a Xbox 360/PC achievement and a PlayStation 3 Trophy.

Retrieve a G.E.C.K. from Vault 87.

Enter Vault 87
Depending on your choice during Picking Up The Trail, you either have to fight your way through Murder Pass to the vault door and enter or you find yourself directly inside the vault.

Find a G.E.C.K.
Both entrances of Vault 87 lead to the Reactor Chamber. From there, you proceed to the Living Quarters, then the Test Labs. There, you eventually encounter a literate Super Mutant named Fawkes who asks to hold a conversation with you over the intercom. Fawkes explains her upbringing in the vault and how she has become literate and civilized through continued access to the vault's database. Fawkes promises to retrieve the Garden of Eden Creation Kit from the irradiated halls above if she is released.

The radiation level where the G.E.C.K. is stored is extremely high. You can proceed in one of two ways: If you hired/bought Charon as a follower and ask him to get the G.E.C.K, he will refuse. The room with the G.E.C.K. can be found by going left from Fawkes' cell. If you release her, she leads you to it and will engage the remaining enemies in melee.
 * Attempt to get the G.E.C.K. without help. If you choose to do so, you will need about 10 Radaway and a good set of armor with at least 20 RAD protection to survive the radiation inside the G.E.C.K. room. (Note: there is an advanced radiation suit in this area that, combined with a rad-x, minimized the received radiation. This means that radaways are not needed).
 * Release Fawkes, who will assist you in both combat and obtaining the GECK, thus fulfilling the objective of the quest. See Free Fawkes below.

(Note: Once you reach the G.E.C.K you have the choice to either take it or activate it. The player is killed upon activation, returning you to the earliest check point.)

Escape from Vault 87
Unfortunately, even after all this effort you will be incapacitated upon attempting to leave the vault by a contingent of Enclave soldiers and the G.E.C.K. will be taken from you.

(Optional) Free Fawkes
You can release Fawkes in one of these ways:
 * Unlock Fawkes' room by picking the Very Hard lock on the door or by hacking the Hard locked computer console next to her door.
 * It is possible these methods do not work because you are either told that the door requires a key or that there is a door lock malfunction.
 * Go down the hall to your right, past 2 Centaurs and into a maintenance room with 2 Super Mutants. Here you will find the Fire Control Console.  Next to it is an Average locked computer console that can release individual cells.  Fawkes' cell is number 05.
 * Activate the Fire Control Console, thus releasing Fawkes and every other inhabitant of the other locked cells.

The rooms contain...
 * Room 01 - 3 dead people (2 Wastelanders and 1 Raider)
 * Room 02 - vacant (Centaur possible)
 * Room 03 - The only "dangerous" test subject, a nutty human named Sid in room 3. He may be friendly if you have not unlocked all the rooms, but will turn hostile once all doors have been unlocked.  If you approach him while he's still friendly, you can try to talk to him, but he just says 'Get out of my head!  Get the fuck out!  Arrg!'
 * Room 04 - vacant (Centaur possible)
 * Room 05 - Fawkes

Followers
If you are accompanied by a follower NPC, they will not be with you after you have been incapacitated by the Enclave. Be sure to retrieve any equipment from them you do not want them to walk off with (as if they were fired) before this happens, or right after retrieving the G.E.C.K. You will not have a chance to re-hire your companion until after The American Dream.

It is not necessary to release your companions before the scripted event however. They are not killed by the Enclave, instead they return to their default locations soon after you escape the Enclave. For example, Dogmeat will be waiting by the Vault 101 entrance. They also still have all the equipment you have given them. You have to do any necessary Karma checks again though and Fawkes may be a more desirable companion anyway if you have chosen to free her.