We all now the first flight with a heavier-than-air aircraft was conducted by the wright brothers in 1903, but when did the first aircraft model made for air-to-surface/air-to-air combat (not modified from a civilian aircraft) first see the light of day?
The Vickers Company of Britain began experimenting with putting machine guns on various types of aircraft in response to a British Admiralty requirement for an aircraft that could take an offensive role. The contract was awarded on November 19, 1912. This resulted in the E.F.B. 1 "Destroyer" of February 1913.
It crashed on its first flight and development continued, resulting in the F.B. 5 "Gunbus", the world's first operational fighter plane. The F.B. 5 first shot at a German Taube plane with its machine gun (which then promptly jammed; the observer then shot at the enemy plane with his rifle, possibly downing it) on Christmas, 1914. It entered widespread service in February of 1915.
Sources:
The British Fighter Since 1912, by F.K Mason
Vickers Aircraft Since 1908, by C.F. Andrews and E.B. Morgan