In a modified version of Rubinstein's bargaining game, two players expect the random arrival of a third party, from whom one of them will receive an interim disagreement payoff in every period until an agreement is finally reached. Each player thinks that his own probability of receiving the disagreement payoff is greater than that assessed by the other player; that is, they are mutually optimistic. We show that when the level of optimism is high and not very durable, equilibrium agreement is delayed until the uncertainty is fully resolved. The efficiency loss caused by such a delay remains substantial when the players are extremely patient.