The Chain is linked by a series of moves. As one couple moves out of their current residence to live in posher quarters another moves in and so it goes all the way up to the lavish mansioned owned by self-made millionaire Leo McKern. The cycle starts all over again when McKern wishing to be closer to his roots returns to the working-class neighborhood whence he came. Each move is wryly commented upon by the team of professional movers headed by Warren Mitchell.