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Kevin Chappell holding off Branden Grace, John Huh in Texas

SAN ANTONIO -- Kevin Chappell birdied three of his final five holes and took a step closer to his first PGA Tour victory with a 1-under 71 on Saturday, giving him a one-stroke lead after three rounds of the Valero Texas Open.

Chappell is 8 under through 54 holes. He's ahead of first-round leader Branden Grace, who rallied with a 2-under 70, and John Huh. After an eagle-birdie finish, Huh shot 71.

Ryan Palmer, a West Texas native who cut through winds as strong as 25 mph, had the round of the day with a 4-under 68. He's joined at 6 under by second-round co-leaders Bud Cauley (74) and Tony Finau (74), Sweden's Carl Pettersson (71), 2013 Texas Open champ Martin Laird (71), Kevin Tway (72) and Australian Cameron Smith (73).

Chappell tied for seventh with Rory McIlroy at the Masters this month, and he got his late charge going Saturday after leaving an eagle putt short at the par-5 14th. He tapped in to gain a stroke, and he made good two holes later with a 12-foot birdie. He chipped to 2 feet on the 318-yard 17th downwind and had another tap-in birdie.

Chappell, 30, flirted with trouble on the 18th when his second shot rolled next to a brook, but he had enough room for a full swing and reached the green to set up a two-putt par.

Grace lost his early tournament lead with a 2-over 73 in the second round. But the South African rallied Saturday and had a lead until a bogey at No. 15.

Gusts that blew past 20 mph kept scores high -- there were 14 scores below par Saturday. On Friday, 49 rounds were under par, and 69 under-par scores were recorded Thursday.

As notable as Palmer's round was in the windy conditions, it fits with the Texans' profile at this course. Since the tournament moved to TPC San Antonio's Greg Norman-designed Oaks Course seven years ago, Palmer's got three top-10 finishes, including his best of a fourth-place tie last year.

With the wind at his back, he drove the 318-yard 17th hole but was faced with a 93-foot eagle putt. He sank a 56-foot putt to birdie earlier at No. 6, so he two-putted for the birdie at 17 and ran in another birdie at 18.

Palmer, originally from Amarillo, hasn't won since Hawaii in 2010.

With these conditions, it didn't take long for the second-round leaders to back up. Cauley bogeyed the first hole, and his co-leader Finau parred until bogey at No. 7 and a double-bogey on the next hole after he was chipping for birdie from right in front of the green.

Cauley later was penalized a stroke when he double-chipped at No. 12 -- he hit the ball a second time on the follow through of his green-side chip. He putted from 13 feet to save bogey.