Henry holed a 50-foot pitch shot for an eagle at his final hole, the par-5 ninth at the TPC-Summerlin course.
The layout has become known for producing some of the lowest scores of the year on the PGA Tour and Thursday's opening round was no exception. More than half of the 132-man field field broke par.
Former U.S. Open champion Webb Simpson shot a 64 and was in fifth place by himself.
Jimmy Walker, who won the opening tournament of the PGA Tour's 2014 season at last week's Fry.s com Open, shot an even-par 71.
Henry, who turned professional 15 years ago, has won twice on the PGA Tour. His most recent victory came at the 2012 Reno-Tahoe Open.