Prep Chicken: Pat the chicken thighs dry with paper towels. Trim any excess skin or large pockets of fat, but leave most of the skin on for flavor.
Make Glaze: In a medium bowl, stir together the brown sugar, soy sauce, and garlic until the sugar is mostly dissolved and you have a thick, glossy mixture.
Arrange: Arrange the chicken thighs in a single layer in a 5- to 6-quart slow cooker, skin side up, with the bones tucked neatly so they fit snugly in the bottom.
Coat: Pour the brown sugar mixture evenly over the chicken, making sure each piece is coated and letting the extra sauce pool around the thighs.
Cook: Cover and cook on LOW for 4 to 5 hours, or on HIGH for about 2 1/2 to 3 hours, until the chicken is very tender and reaches an internal temperature of at least 165°F near the bone.
Broil (Optional): For a more caramelized look, carefully transfer the cooked thighs to a foil-lined baking sheet and broil them skin side up for 3 to 5 minutes, watching closely, until the tops are browned and the glaze is bubbling.
Thicken Sauce: While the chicken is under the broiler (or resting), skim off any excess fat from the surface of the sauce in the slow cooker. If you’d like it a bit thicker, turn the slow cooker to HIGH and let the sauce bubble uncovered for 10 to 15 minutes, stirring now and then, until slightly reduced and glossy.
Serve: Return the chicken to the slow cooker, spoon some of the warm sauce over the top so the thighs are glazed and surrounded by the caramel-colored juices, and serve hot with extra sauce on the side.