This paper explores, within the context of a continuous-time noncooperative game, how time and information affect the rational behavior of bargainers. In the model, a buyer and a seller are engaged in the trade of a single object. Both bargainers have private information about their own preferences and are impatient in that delaying agreement is costly. The rules of the game stipulate that at any time a player can either make an offer or accept the most recent offer of his opponent. In choosing their strategies, the bargainers are unable to make binding commitments; thus, each players strategy must be optimal at every instant given his current beliefs about the preferences of his opponent. In equilibrium, the bargainers communicate their private information by exhibiting their willingness to delay agreement. A player expecting large gains from trade is more impatient than one expecting small gains, and hence makes more attractive offers, which are accepted earlier in the bargaining process. Trade occurs whenever gains from trade exist, but due to the incomplete information, often only after costly delay. Thus, the model provides an explanation for the inefficient bargaining behavior that is frequently observed in practice.