Chalmers followed a first-round 67 with a second-round 72 for an 18-hole total of five under at the Country Club of Virginia at Richmond on Saturday (Sunday AEDT).
Compatriot Bransdon carded a second-round 69 after opening with a 70, to also sit at five under.
They are four shots behind American Ken Duke, who followed a dazzling front nine with a relatively uneventful second nine holes to take a one-stroke lead after two rounds.
Duke carded a six-under-par 66 to move to nine under 135, one shot better than Argentina's Ricardo Gonzalez, who fired a five-under 67.
South African Retief Goosen, who led after the first round with a 66, posted a 71 and is tied for third at seven under with American Steve Flesch (70 on Saturday).
The tournament is the first leg of the Charles Schwab Cup Playoffs, the climax of the PGA Tour Champions season.
The top two players in the points race, South African Ernie Els and Australian Steven Alker, are well back. Els is tied for 30th at one under after a 72, and Alker (75 on Saturday) is tied for 48th at two over.
Only the top 54 players after this event qualify for next week's tournament.
Duke, who began the week at No. 29 in the standings, went five-under 31 on the first nine holes. He made birdies at the second, third, fourth, sixth, eighth and ninth, with his lone bogey at the par-4 seventh.
Six consecutive pars followed on the back nine until a birdie at the par-5 No.16.
"You've got to drive it in the fairway and I do that, but I have to birdie the par-5s," said Duke, who birdied the par-5 sixth, ninth and 16th. "These guys hit it too long for me. I think I got three of 'em today and three yesterday and that's a bonus."
Duke has, through 36 holes, hit 23 of 28 fairways and 27 of 36 greens in regulation.
His lone PGA Tour Champions victory in 133 starts entering this event was the 2023 Rogers Charity Classic.
Two other Australians are under-par at the halfway point, with Rod Pampling rebounding after opening with a 74 to card a second-round 67 and sit at three under.
Stuart Appleby (71, 71) is one shot further back at two under.
Mark Hensby (72, 73) and Michael Wright (78, 67) are one over, Cameron Percy (71, 75) and John Senden (72, 74) are two over, Richard Green (73, 76) is five over, and Steve Allan (73, 78) is seven over.
- with AAP
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