Look at this:
The chain seems to be moving with a uniform velocity. Is the kinetic energy of all the moving beads in the whole chain (at the time they reach the ground) the same as the kinetic energy (when touching the ground) of the whole chain when you let it fall freely from the same height as the jar? Or move the beads in the chain with the velocity a single bead would have (when reaching the ground) as you let it fall from jar height? In both cases, the chain possesses the same potential energy.