Chopra, who shared the third place with Steve Stricker, Ernie Els and Chris Stroud, was one shot behind Ken Duke and Cameron Tringale, who carded seven-under 65 each.
Defending champion Bubba Watson was six strokes back in his first tournament since winning the Masters.
Chopra, a two-time tour winner who has failed to make the cut this season, put himself in position to regain full-time status.
His 66 was his first round in the 60s this season.
"The game has been fine, the results have been frustrating," Chopra said.
"The harder you press in this game the tougher it gets and when you get momentum going one way or the other, it's hard to break it, and I've been handling it the wrong way," the Swede added.
Chopra had a bogey free round with three birdies on either side of the TPC Louisiana Course. He had birdies on third, seventh and eighth and then 10th, 11th and 17th.
Ben Cutis, the Valero Texas Open winner in San Antonio, was another shot behind at 68 along with John Rollins and Jason Dufner. World number two Luke Donald opened with a 73. PTI Cor SSC