It is impossible to carry the ball and chain through to the next level; you must drop it whenever you go through a door.
I'll bet this is to prevent a bug in which you have TWO ball and chains attached to you, since the game probably does not track the ball & chain in your hands. It will probably not detect a ball & chain trailing you, and attach another o.O.
Also they game is coded not to let you carry any "heavy" items threw the door.