Phil Mickelson, With First-Round 63, Breaks Course Record at British Open

TROON, Scotland — Phil Mickelson broke the course record at Royal Troon with a round of eight-under-par 63 on Thursday, opening a three-shot lead at the British Open on a day when favorable conditions led to a run of low scores.

Americans held seven of the top eight places on the leaderboard when Mickelson finished at 18. Mickelson’s round could have been even better: His birdie attempt at the final hole circled the cup and then hung tantalizingly on the lip as Mickelson put his hand over his mouth in disbelief.

The birdie would have been his ninth of the round — against no bogeys — and would have produced the first round of 62 at a major championship. Instead, he wound up tied with dozens of…