Martin's 16-point haul was the best round of the day, while Woodland tallied 11 points to stay in the hunt for the title. Scot Martin Laird is fourth on 28 points after a six-point round.
The format awards eight points for an albatross, five for eagle, two for birdie, zero for par, and subtracts a point for bogey and three for double-bogey or worse.
The 42-year-old Chalmers began the day with a two-point lead over Woodland and although the Australian bogeyed his opening hole, he rode a hot putter thereafter to rebound with eight birdies.
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World ranked 490th, Chalmers has conditional status on the PGA Tour and remains without a victory on the North America-based circuit in 385 career starts.
"There's a long way to go, and there's plenty of players capable of shooting a lot of points out here," said Chalmers, whose last victory was the 2014 Australian PGA Championship.
"I'll get out there tomorrow and get that first tee shot in play and get after it."
Also at stake for Chalmers and many of the other leading contenders is a spot in the British Open at Royal Troon later this month after next week's event, the Greenbrier Classic, was called off due to flooding in West Virginia.
The British Open exemption normally available at that event was subsequently transferred to the leading player at Reno who does not already have a spot.
Woodland is the only golfer in the top-20 who has already qualified for Royal Troon.
(Reporting by Tim Wharnsby; Editing by John O'Brien)
