Action from the 1908 Chiasso Cup Final
Associazione Calcio Milan was formed in 1899 by a group of Englishmen as a football and cricket club. The use of Milan as opposed to Milano in the name reflects these origins. In 1908 (by which time Milan had been Italian champions three times) the club split over a disagreement about the limited opportunities open to foreign players (ironic, given their origins). This led to a breakaway club being formed- Internazionale. Internazionale won the championship within 2 years of their foundation. Milan, on the other hand, went into decline and didn't win the league for another 40 years.
The Derby della Madonnina, as the Milan derby is known, is one of the greatest rivalries in the world. The first meeting of the two clubs on 18th October 1908, eight months after Inter's formation, didn't take place in Milan, but in Switzerland. The match was the final of the Chiasso Cup (the third edition of this international club tournament, which Milan had won on both previous occasions). It was a game of two 25-minute halves, played in front of 4,000 spectators.
Milan won 2-1.
Milan lined up: Root; Glaser, Hall, White, Steltzer, Meschia, Lana, Madler, Forlano, Laich, A. Colombo.
I cannot find a record of the Inter team.