When Mickey runs toward the camera, trying to get away from the cops, his chain suddenly disappears and is not seen at all for the rest of the film. He can not have taken it off, as it would be impossible to do without a key.
After Mickey gets over the prison wall, he tries to run away, but is pulled back by the weight of the ball and the chain breaks, yet Mickey still carries the ball when he could just run away and leave the ball.