Ed Dougherty, Lon Hinkle, Rodger Davis, last year's runner-up Jim Colbert and 2000 champion Hubert Green share third at 1-under-par.
Quigley birdied the opening hole at Club de Golf Chapultepec when his drive at the 316-yard hole left him only a chip on to the green. He converted the five-footer and added another birdie at four after he holed a 12-footer.
The 54-year-old played steady golf over the middle of his round with nine pars and a three-putt bogey at No. 10. Quigley closed his round with a five-foot birdie at 15 and at 18 he ran home a 20-foot birdie putt that left him the only player in the field to shoot a round in the 60s.
'I was pleased to just keep it under par,' said Quigley, who shared the first-round lead of last week's Verizon Classic before he tied for seventh. 'I'm extremely happy with 3-under-par. I think 6-under for the tournament would be a very good score.
'I knew scores wouldn't be too low on this course,' said Quigley, referring to the first-time host of this event. 'The greens were a little more difficult to putt and the wind was tricky today.'
Quigley has enjoyed quite a bit of success so far in his 2002 campaign. His final-round 73 last week was his only above-par round on tour this season and he has three top-10s out of the gate.
Hall birdied one but gave the stroke back with a missed 15-foot par save at the fourth. It was at the end of his round when Hall moved into second place and it was solid iron play that got him there.
At the 164-yard 17th, Hall used an 8-iron to get eight feet from the hole and set up birdie once again breaking into red figures. He took sole possession of second place when his 9-iron on 18 landed six feet from the hole, where he calmly stroked home the birdie putt.
'Obviously 2-under is a good score for this golf course,' said Hall, who started the season strong with a pair of top-10 finishes. 'You cannot attack this golf course. Don't try to force it.'
Bruce Fleisher and Christy O'Connor are part of a logjam at even-par 72. Hale Irwin, the record-holder for wins on the Senior Tour, opened the tournament with a 1-over-par 73 and was joined by defending champion Mike McCullough.
Full-field scores from the Audi Senior Classic