Hill stands at 11-under-par 133 through 36 holes. First-round leader and defending champion Larry Nelson is in solo second place at 10-under following a 3-under-par 69.
Mike McCullough (65) and Allen Doyle (69) are tied for third place at 9-under.
The 62-year-old Hill is in search of his 19th career Senior PGA Tour title, and his first since 1996.
Saturday, Hill recorded four birdies in a five-hole stretch beginning at the par-4 6th. The lone blemish on his card came way of a bogey-6 at the par-5 9th.
Nelson is vying for his third victory of the season, but his first since February.
Full-field scores from the FleetBoston Classic