By Mark Lamport-Stokes

SAN FRANCISCO (Reuters) - The U.S. Open lived up to its reputation as the toughest championship of all in the early going on Thursday with only five players under par in the opening round.

On a cool hazy day at the Olympic Club, American Kevin Na was alone at two under after six holes, a stroke in front of South African Branden Grace and Americans Jason Bohn, Joe Ogilvie and Davis Love III.

Grace, a three-times winner on the European Tour this year, had completed six holes and Bohn five while Ogilvie and U.S. Ryder Cup captain Love had 14 holes to play.

Three-times U.S. Open champion Tiger Woods was among a large group locked at even par, having parred his first five holes after teeing off at the par-four ninth.

Seeking his first major title in four years, Woods was playing in a glamour grouping with fellow Americans Phil Mickelson and Masters champion Bubba Watson who were both struggling at two over.

Left-hander Mickelson, runner-up a record five times at the U.S. Open without yet landing the prestigious trophy, got off to the worst possible start when he hooked his opening tee shot and lost his ball.

He did well to bogey the hole after hitting a third shot off the tee but went on to bogey the next two holes, finding a greenside bunker with his approach at the 10th and missing a par putt from four feet at the 11th.

However, Mickelson partially recovered when he birdied the par-three 13th to get back to two over.

Fellow left-hander Watson bogeyed the ninth and 11th to lie four strokes off the early pace on a par-70 Lake Course layout boasting arguably the toughest stretch of holes in major golf from the first to the sixth.

Defending champion Rory McIlroy of Northern Ireland was among the day's late starters, scheduled to tee off at 1:29 p.m. (2029 GMT) with world number one Luke Donald and third-ranked Lee Westwood.

(Reporting by Mark Lamport-Stokes in San Francisco; Editing by Frank Pingue)