- Jun 6 Haitian explorer Jean Baptiste-Pointe Dusable settles in Chicago
- Jun 9 1st Protestant church west of Pennsylvania (in Ohio) holds communion
- Jun 9 1st naval attack of Revolutionary War takes place in Providence, Rhode Island
- Jun 10 Burning of British revenue cutter Gaspée by Rhode Islanders
- Jun 12 Marion du Fresne is killed at Tacoury's Cove, Bay of Islands, New Zealand, by local Māori
- Jun 22 Somerset v Stewart court case finds slavery unsupported by English common law, encouraging the abolitionist movement