Bransdon fired a five-under 67 to be joint fifth, one behind first-round leaders Woody Austin, Steven Alker, Robert Karlsson and Gene Sauers at The Club in Snoqualmie Ridge.
The 50-year-old from Melbourne enjoyed six birdies to go with one lone bogey.
Green, who has been a model of consistency on the Tour this year including a second-placed finish at the Senior PGA Championship, a third at the US Senior Open Championship and a runner-up at the Senior Open at Carnoustie, shot a four-under 68.
He is one ahead of compatriot Chalmers, who had a quadruple bogey eight on the fifth and an eagle on the 18th in a topsy-turvy 69, that also included five birdies.
Austin, who is seeking his fifth win on the Champions Tour, made eight birdies, including two in his final three holes, to keep pace with the other leaders.
The 60-year-old has three top-five finishes at this tournament.
"Just made a few putts, that's all," Austin said. "Played really solid. Three-putted the first hole right out of the gate, but then ... I think I might have hit two bad shots all day."
"The golf course isn't the hardest obviously, so there's always some good rounds out there, but you do still have to drive it straight," Austin said.
"I don't think I missed a fairway today, so that's pretty important. ... I think that's the first time in a while I haven't missed a fairway."
New Zealander Alker, who entered the week third in the Tour standings, finished strong with an eagle on the par-5 18th hole during his bogey-free round.
The 53-year-old is seeking his ninth career win on tour. With a win this weekend, he would join Ernie Els, Richard Bland, Padraig Harrington and Stephen Ames as multi-time Champions winners this season.
"I like poa greens. They're always fantastic here, they're always rolling so good. It's just a matter of getting your speed and you hit 'em online and you hole 'em," said Alker.
Karlsson, 54, shot a bogey-free round and finished with six birdies. He has yet to earn a win on the Champions Tour, settling for second five times.
Sauers made a late charge, notching birdies on Nos.14, 15 and 16 but stumbled on No.18 with his only bogey of the day. He tied his lowest score in a round this year and is in search of his second career Champions win. Sauers, 61, won the US Senior Open in 2016.
Kirk Triplett and Michael Allen joined Bransdon on 67.
Defending tournament champion Stephen Ames struggled most of the day after making bogeys on No.11 and No.17 and a double bogey at No. 4. The Canadian finished one-under 71 and is tied 26th.
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