Note: This secret cannot be reached after dropping down the hole in the first room. In the starting area there are three alcoves each in the walls to the left and right. The third one on the left has a armor bonus in it; lower it like a lift and follow the stairs down to an area with a backpack and chainsaw. The secret only seems to trigger when you're leaving the area by riding the lowered floor back up to the starting room.
There is a hallway shaped roughly like a "T" turned 90 degrees to the left in the northwest corner of the map. You enter from the eastern arm, and the southern arm is blocked by a locked door (the switch to open it is located in an area beyond the northern arm, but that's not important to finding this secret). One of the stone wall on the eastern wall of the souther arm of this "T"-shaped hallway is solid gray, and lacks the green highlights of the surrounding walls. Open it to get a soul sphere.