Quigley and Hill shot 7-under 64s on the TPC of Tampa Bay to lead Bruce Summerhays by one shot. Tom Kite and 2000 champion Bruce Fleisher are each two back, while Bruce Lietzke and Doug Tewell opened with 67s.
Kite is vying for his second victory of the year, having won the season-opening MasterCard Championship.
Hill won this event 12 years ago. The 18-time tour winner hasnt triumphed since 1996, though that came at the age of 57. The now 63-year-old started Friday with four straight pars, but birdied his final five holes on the front side, and then added two more to his card on Nos. 11 and 12.
Hills 64 was one shot off his career low round, and one shot from making him the youngest player to match his age in tour history.
'Trying to shoot your age every time you go play has got to be some kind of inspiration,' Hill said.
Quigley, playing in his 156th straight senior event, birdied holes 4-7 to make the turn in 4-under 31. He went on to birdie three more holes, including the par-4 18th, coming home.
'I equate this to poker or casino gambling,' said Quigley. 'When you're on a roll, you've got to go for it. I tried to make birdie on every hole.'
Last weeks winner, Hale Irwin, is four back after a 68. Defending champion and reigning rookie of the year Bob Gilder shot 2-over 73, as did Allen Doyle and 1999 winner Larry Nelson.
Many of the tour's big names are in attendnace this week. Fuzzy Zoeller and Lee Trevino each shot 68. Ben Crenshaw and Gary Player posted even-par 71s. Arnold Palmer, making his seasonal debut on the senior circuit, shot 11-over 82.
Full-field scores from the Verizon Classic