Gilmer ended their basketball season 3-7 in district, while Chapel Hill will continue in the playoffs with a 7-3 record.
Bullard and Tatum are the other two playoff teams in District 17-3A this year.
As usual, the Buckeyes had a cold quarter.
Tuesday night they opened the match unable to penetrate the hoop as Chapel Hill jumped out to a 12 -2 lead before J.T. Beecham hit a 3-pointer late in the quarter to cut the lead to 12-5.
In the second quarter, the Buckeyes started hitting the basket as four players contributed.
Daniel McLaren led the way by scoring six points, and Zach Jones added three from downtown.
When Tevin Godfrey hit a layup at the buzzer following a steal, Gilmer trailed the Bulldogs 24-18.
Tristen Holt found his range in the second half, as he scored six of his team-leading 13 points in the third quarter of the match.
Jones and McLaren also contributed to the effort as the Buckeyes cut the Chapel Hill lead to two, 32-30.
After the teams traded goals to open the fourth quarter, Holt converted a steal into two points, tying the game at 34-34 with 6:03 remaining in the game.
After McLaren grabbed a defensive rebound, Holt put the Buckeyes ahead with a 3-point play. With 5:26 to go, Gilmer led 37-34.
With 4:20 remaining, Holt hit an impossible over-the-left-shoulder behind-the-back layup for a 39-36 lead.
Chapel Hill responded from the charity stripe with LaDedrick Calico hitting one free throw and Matthew Tucker two to tie the game at 39-39.
Long balls by Jones and Caleb Denton kept the Buckeyes close, but Jordan Williams sealed the deal for the Bulldogs from the free-throw line.
Williams went 8-for-12 in the fourth and 9-for-14 for the night to win the game for Chapel Hill.
He finished with a game leading 14 points, Andrew Tucker with 11; Kenson Tave, eight; and Matthew Tucker, six.
Jones had 10 points in his final game for the Buckeyes, Tevin Godfrey, two; McLaren, eight; J.T. Beecham, five; Kavin Potter, four; and Denton, three.