The number and strategic significance of offshore drilling rigs owned and operated by multinational corporations make them attractive terrorist targets. Jurisdiction over terrorist attacks on offshore drilling facilities is clearly assigned to the coastal state by international law. Should the 1982 draft Convention of the Law of the Sea enter into force, this legal jurisdiction would be extended seaward to 200 nautical miles for those states party to the treaty. In all likelihood, terrorist attacks on offshore rigs would not be considered piracy under international law. Such attacks would most aptly be under the jurisdiction of the coastal state's law enforcement agencies. A Coast Guard-like force trained in antiterrorist tactics would be particularly well suited to this task. The best strategy for offshore maritime terrorism is overt deterrence through premeditated prevention. Rig employee background checks, access control, and the inspection of materials brought onto the rig are appropriate preventive steps. Simulation exercises involving mock terrorist attacks would be an effective training device. Sixty-eight footnotes are provided.