First you need to go to Edward's optional mission which is contained in chapter 5.

Then clear the second trap room (which gives you engine room access) and grab the alien artifact. It will be at the bottom of the stairs, by some boxes, on the right side of the door.

Save your game and quit. Then go back to the same room.

Once you are back in that room, run from there to the room that contains the sign "Storage Unit F-199". This will refresh and regenerate the alien artifact you already have.

You are then free to go back and get it again.

Youtube: http://goo.gl/6U5Fr