Preheat the oven to 425°F (220°C). Place the roasting pan in the oven while it heats so the pan is hot when the chicken goes in.
Rinse the chicken and pat it dry with paper towels. This helps the skin crisp up. Rub the outside with olive oil, salt, pepper, and thyme. If you have time, let it sit for 15 minutes to 30 minutes for the flavors to start soaking in.
In a small bowl, whisk together the apple cider, brown sugar, and minced garlic until the sugar mostly dissolves. This will be your glaze and baste as the chicken roasts.
Place the chicken breast-side up in the hot roasting pan. Tuck the wing tips under and loosely tie the legs if you like. Pour about a quarter of the glaze over the chicken to glaze the skin.
Roast for about 45 minutes, then baste with the remaining glaze. Continue roasting until the internal temperature reaches 165°F (74°C) in the thickest part of the thigh and the skin is deep golden and crisp, about 15 to 25 more minutes depending on your oven and chicken size.
Remove the chicken from the oven and let it rest for 10 minutes before carving. This helps the juices redistribute, so slices stay moist.
Meanwhile, pour any pan juices into a small saucepan. If you want a thicker glaze, simmer it for a few minutes to reduce slightly. You can spoon a little glaze over the slices when serving, if you like a glossy finish.