Chalmers recovered from an outward nine of 37 to be home in four-under 31 for an opening round of 68 over the par 70 TPC Four Season’s Resort layout.
Alongside Chalmers in a tie for 14th are Leishman and Day, who also bounced back from a slow start with a homeward nine of 32.
Rod Pampling, who like Chalmers is a resident of the Dallas area, opened with a round of 69, while another Dallas-based Australian, Stuart Deane, produced a round of even par 70.
New South Welshman Brett Drewitt opened with 72, Cameron Percy, Geoff Ogilvy and Matt Jones 73, Stuart Appleby 76 and the struggling Steven Bowditch, who won this event in 2014, shot 80.
Among the favourites this week, Dustin Johnson is in a share of eighth position at three-under, Jordan Spieth is two-under, while defending champion and reigning Masters winner Sergio Garcia struggled to a three-over round.