Two share lead in Portugal with 65
Fisher made birdies on three of his first six holes and then birdied four of the first five holes on his back nine.
Gallacher shot a bogey-free round.
The co-leaders were followed by George Murray of Scotland at 5 under.
Martin Kaymer, who holed the putt that kept the Ryder Cup with Europe less than two weeks ago, shot a 69 on the Oceanico Victoria Golf Course.
Ryder Cup teammate Francisco Molinari finished at par, while Europe captain Jose Maria Olazabal was 4 over.
Copyright 2012 by The Associated Press