Compton is competing at Southern Hills Plantation in Brooksville, Fla., one of four sites for the second-stage of PGA Tour Q-School.
Josh Teater holds the 54-hole lead at 12 under. Compton stands at 7 under.
Compton, just six months removed from his second heart transplant and who is being granted the use of a golf cart during Q-School, needs to finish among the top 20 and ties to advance to the final stage in early December in La Quinta, Calif.
Compton is coming off a tie for 60th at last week's Children's Miracle Network Classic in Orlando, where he was playing on a sponsor's exemption.