Chester is always one of three mobs at the spot mentioned above. (I don't think you can fall off the bridge. I've tried, and haven't found a spot that lets me jump off)
He will either be one of the two 'door guards' on either side of the steps going down, or the roamer that goes down in to the big chamber and back up to the bridge. He is non aggro until you do the turn in.
If he is a door guard, just kill the other door guard and roamer. (Really, you would just need to kill the roamer). If he IS the roamer, just wait for him at the top of the steps. The upper 'landing' area at the top of the steps is a safe spot aside from the roamer.
Be aware, in case someone killed him just before you got there: There is a mob just on the other side of entryway to this area from the bridge. He is the PH for the SoulStripper. If you are waiting for Chester, might as well camp him at the same time. The PH is just a standard mob. The Enraged Soulstealer, on the other hand, is a mean ******* compared to the other mobs in the area. I have always been able to take him with my cleric\shaman duo, but he is definitely meaner than his counterparts. (Of course, if you are decently geared by today's standards, he is going to be a pushover). If Chester runs too much with the Enraged Soulstealer or his PH up, you may well get them as an add.
Nothing special to get Chester to spawn, just keep killing the three PHs. Since you will no doubt be bored, kill everything in the chamber below and on the bridge behind you...but you don't need to to get Chester up. He is fairly rare, but you won't be there for days. A few hours at most.