The chain has become completely loose and will not recoil, ?

You didn't say what model you have, but I believe they are all functionally similar to my Model B rower. There is a "skewer" assembly inside the seat rail with a shock cord and pulley's that keeps tension in the chain throughout its range of travel. To some extent it is adjustable by taking slack out of the shock cord. On mine, this can be done by grabbing the shock cord adjustment mechanism ("SCAM") with pliers and pulling it out of the rear of the machine and adjusting the slack. If it is very loose or you just want to be sure of what is going on, the entire skewer assembly pulls out from the front (flywheel side) of the seat rail after removing four screws that hold it in place. Go to the concept2 website for diagrams, instructions, and parts lists for your model.

SamInRaleigh has it right. I was able to eliminate the slack in my chain by pulling the mechanism out the rear side (seat rail side), and adjusting the bungee cord. Not sure if it works for other models but it sure worked on mine.