Because it is a rear chain, you have a problem because the pantry wall all but eliminates the possibility of access to the adjustment of the chain attach point. I did quite a bit of work on all four of my chains due to broken rollers. The front two were very easy, but the back two were a real challenge, there just isn't much room to work there.
If you look at your front chain guide carrier assembly bolted vertically to the wall you will see a carrier that is actuated by the hydraulic cylinder. The cylinder is bolted to this carrier block that slides the chain either up or down the wall, thus pushing or pulling the over-center locking chain to extend or retract the room slide. There is a threaded bolt attach point that you can make minor adjustments to reduce slack in the chain. I would caution, however, that you check both the extended and retracted chain positioning to make sure the chains are both pushing and pulling the exact amount to assure that the slide remains square to the outside wall.
2006 Alpine 36' FDTS