Gay, a former Louisville, Ga., resident, made six birdies on the front nine, including five in a row from the fourth through eighth holes.
"That front nine was awesome," Gay said.
The birdie barrage helped him to 5-under-par 66 and, at 9-under par, a one-stroke lead over former British Open champion Hamilton.
First-round leader Alex Cejka followed his 64 with 71 and was tied with two-time U.S. Open champion Lee Janzen, two shots behind Gay.
Janzen's round of 70 featured an ace on the 17th hole.
Augusta native Charles Howell (69-74) and Evans resident Vaughn Taylor (71-72) are at 143, or 10 shots off the lead.
Gay has steadily improved over his 11 full PGA Tour seasons. He earned his first career victory at the Mayakoba Golf Classic in Mexico last year and had a personal high of more than $2.2 million in earnings.
Gay's streak began when he rolled in an 18-footer for birdie on the par-3 4th hole, then picked up steam with a 25-foot putt a hole later. His approach from a fairway bunker landed inside 5 feet for a third consecutive birdie.
After a birdie putt inside 10 feet on the seventh, Gay closed the stretch with a putt of 20 feet to reach 10-under.
Gay had a chance from 15 feet away on the ninth hole to keep things going, but settled for par.
Gay made his only bogey on the 10th hole, then parred in to hold on to the lead at Harbour Town Golf Links.
He's had his struggles in Hilton Head, missing the cut six times in his nine previous trips. And Gay felt as challenged Friday with the swirling winds, despite his charge.
"Heck, I was as surprised as anybody" about his birdie run, he said.
Two-time defending champion Boo Weekley shot 70 and is eight shots off the lead.