Grease a large slow cooker with cooking spray. Roll a few small balls of aluminum foil and place in slow cooker, creating a rack for the chicken.
In a small bowl, whisk together brown sugar, chili powder, paprika, and thyme.
Pat chicken dry with paper towels and season generously with salt and pepper. Rub brown sugar mixture all over chicken, then place in slow cooker, breast side up.
Cook on high for 2 ½ to 3 ½ hours, until the juices between the leg and the thigh run clear or a thermometer inserted into the thigh reads 165°.
Remove chicken from slow cooker. To crisp up the skin, transfer chicken to a large baking sheet and broil until golden, 3 to 4 minutes. Let rest 10 minutes before slicing and serving.