He finished with six birdies overall, before rolling in a 17-footer for an eagle on the par five ninth.
The 41-year-old five-time Ryder Cup player is joined at 10-under par by unheralded compatriots John Peterson, Tom Hoge and Talor Gooch while four-time PGA Tour victor Kirk is also in contention at the same mark.
"I can't remember when, or if, I've ever made three eagles in a round but it was fun", said Grace, who eagled the second, eighth and 15th, all of them par fives.
Johnson got off to a hot start in his pursuit of Kirk, with birdies at the first three holes.
Kirk grabbed an eagle at the 10th on his way to a three-under 67, while two-time major victor Johnson matched that round and like Harman, sank an eagle on the ninth. "I've always kind of felt like as long as there's fairways and green and holes to putt it, then I'm going to be fine".
"Definitely an up and down day", Kirk said.
"I'm making putts, but I'm also putting myself in position to make those putts", Harman said.
Harman played in the final group at Kapalua last week and tied for third in a final round in which no one had much of a chance against Dustin Johnson.
"I had a great day today, and I'm about to go do it".
Harman had been solid before making three straight birdies, beginning at the second.
Vaughn Taylor fired six birdies in his six-under 64 and was tied with Brian Harman, Kyle Stanley and Talor Gooch. Harman, playing in the afternoon, had eight birdies that included three in a row at the fifth, sixth and seventh.
Peter Malnati, Daisuke Kataoka, Matt Every and Tom Hoge opened with 5-under 65s.
Defending champion Justin Thomas opened with a three-under 67, as more than half of the field - 77 players - broke par.
World number four Thomas had Phil Mickelson's former caddie Jim "Bones" McKay on his bag, filling in for regular caddie Jimmy Johnson, who is sidelined by plantar fasciitis.