The Offaly man finished the round with 68, aided by two birdies on the back nine.
Rory McIlroy also has some improving to do if he's to challenge the leaders, Justin Day and Brendon Todd at five under par.
McIlroy shot a round of 70 and sits at level par for the opening of the second round in San Francisco.
Graeme McDowell is currently 2 over par.
Tiger Woods, who is in a group with McIlroy and world number one, Justin Thomas, is four shots behind the leaders.
The 15-time major winner, shot a two under par 68, his lowest opening round in a major since 2012.
Woods said it was a satisfying start to the tournament.