The authors report on a finding that annual U.S hurricane counts are significantly related to solar activity. The relationship results from fewer intense tropical cyclones over the Caribbean and Gulf of Mexico when sunspot numbers are high. The finding is in accord with the heat-engine theory of hurricanes that predicts a reduction in the maximum potential intensity with a warming in the layer near the top of the hurricane. An active sun warms the lower stratosphere and upper troposphere through ozone absorption of additional ultraviolet (UV) radiation. Since the dissipation of the hurricane's energy occurs through ocean mixing and atmospheric transport, tropical cyclones can act to amplify the effect of relatively small changes in the sun's output thereby appreciably altering the climate. Results have implications for life and property throughout the Caribbean, Mexico, and portions of the United States.