The paper studies a strategic sequential bargaining game with incomplete information: Two players have to reach an agreement on the partition of a pie. Each player, in turn, has to make a proposal on how the pie should be divided. After one player has made an offer, the other must decide either to accept it or to reject it and continue the bargaining. Player 2 is one of two types, and player 1 does not know that type player 2 actually is. A class of sequential equilibria (called bargaining sequential equilibria) is characterized for this game. The main theorem proves the (typical) uniqueness of the bargaining sequential equilibrium. It specifies a clear connection between the equilibrium and player 1's initial belief about his opponent's type.