In 1778 France entered the American Revolutionary War (1775–1783) on the American side. Colonel Dillon sailed with his regiment to the Caribbean to campaign against Britain under the command of D'Estaing. In 1779 he and his regiment fought at the Capture of Grenada against British forces under George Macartney. They landed on 2 July, and stormed the Hospital Hill which the British had chosen as the centre of their resistance. Arthur personally led one of the storm parties, his brother Henry led another. Macartney surrendered on 5 July. On 6 July 1779 a British fleet under appeared off the coast of the island and the naval engagement of the Battle of Grenada was fought. In September and October 1779 Dillon fought at the Siege of Savannah where he was promoted brigadier. After the Treaty of Paris, he became governor of Tobago.