The American world number six, who has finished in the top five at his past three tournaments including The Masters, carded a five-under 66 at the Harbour Town Golf Links.
Kuchar is joined by countrymen Scott Langley and William McGirt at the top of the leaderboard, with the trio two shots clear.
Harris English is outright fourth at three under, with a group of 15 players – including 20-year-old Jordan Spieth – a further shot back at the PGA Tour event.
Kuchar, who was tied for fifth at Augusta on Sunday, was consistent throughout the opening round in South Carolina.
He started on the back nine and holed birdies at 13 and 15 before producing three more at the turn, including on his last – the ninth.
Langley would have held the outright lead if not for a bogey at the 18th as he set up his round with a run of six birdies – and a bogey – on the front nine.
McGirt's birdie at the par-three 18th helped him into a share of the lead, while English mixed five birdies with two bogeys.
A host of Americans are in the group at two under, with Scot Russell Knox, South African Rory Sabbatini and Australian Robert Allenby making up the non-local contingent.
Matt Every, Billy Horschel, Bo Van Pelt, Brian Harman, Ben Martin, Tim Herron, Brian Stuard, John Mallinger, Lucas Glover, Kevin Streelman and Charles Howell III are alongside Spieth.
Spieth, who was tied for second at the Masters after sharing the lead heading into the final round, found his consistency on the back nine.
Englishman Luke Donald and South African Charl Schwartzel are locked at one under, while Northern Irish defending champion Graeme McDowell is a shot further back.