The role of strategic delay is analyzed in an infinite-horizon alternating-offer model of bargaining. A buyer and 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. An equilibrium is constructed in which the bargainers signal the strength of their bargaining positions by delaying prior to making an offer. A bargainer expecting large gains from trade is more impatient than one expecting small gains, and hence makes concessions earlier on.