Underwater Acoustic Sensor Networks (UW-ASNs) use acoustic links as a means of communications and are accordingly confronted with long propagation delays, low bandwidth, and high transmission power consumption. This unique situation, however, permits multiple packets to concurrently propagate in the underwater channel, which must be exploited in order to improve the overall throughput. To this end, we propose the Delay-aware Opportunistic Transmission Scheduling (DOTS) algorithm that uses passively obtained local information (i.e., neighboring nodes' propagation delay map and their expected transmission schedules) to increase the chances of concurrent transmissions while reducing the likelihood of collisions. Our extensive simulation results document that DOTS outperforms existing solutions and provides fair medium access.