Leonard opened in 6-under-par 65 to finish the first round one shot off the lead, held by Marco Dawson, who missed almost the entire 2000 season because of back surgery.
Dawson fired his lowest round of the season, a 7-under 64, to earn top honors after Day 1 at La Cantera Golf Club.
Jay Williams, currently 105th on the money list, matched Leonards 65. Brandel Chamblee, Scott McCarron, Carl Paulson and Bob Burns shot 5-under 66 in the first round.
Leonard, who finished second at this event in 1995 and 98, is not only in search of back-to-back wins in his home state, but hes also seeking win No. 1 this season.
The former University of Texas All-American has seven top-10 finishes on the PGA Tour in 2001, with his best performance coming in a tie for fourth at the Shell Houston Open. The following week, he shot 61 in the third round of the Verizon Byron Nelson Classic in his hometown of Dallas, only to shoot 69 on Sunday to tie for sixth.
Thursday, the 29-year-old carded seven birdies and one bogey.
'It probably helped that I played in the afternoon. I had some scores to shoot for,' Leonard said.
'All that defending champion stuff, that's Tuesday and Wednesday. I got into the round today and just basically left last year's tournament behind.'
Dawson also posted seven birdies, but did so without a dropped shot. Playing on a medical extension this year, Dawson is 173rd on the money list.
Its started coming together in the last couple of weeks and this is just a continuation of last week when I played really well, Dawson said in reference to a tie for 22nd at the Marconi Pennsylvania Classic.
My back is probably in better shape than its ever been because I worked so hard to rehab it.
A trio of 2002 Ryder Cup team members are in attendance this week due to the postponement of the matches. Swedens Jesper Parnevik shot 4-under 67, while Americans David Toms and Hal Sutton shot 74 and 69, respectively.
Parnevik, Leonard and McCarron are all trying to step inside the top 30 on the money list, which would earn them a spot in the season-ending Tour Championship.
McCarron is 32nd in earnings, while Parnevik is 33rd and Leonard is 39th.
A host of players are tied for eighth place at 4-under, including former Texas Longhorn standouts David Gossett and Bob Estes. Estes who claimed his maiden PGA Tour victory at this event in 1994.
Full-field scores from the Texas Open