How to Make It
In a small bowl, combine the salt, sugar, thyme, pepper and garlic. Arrange the chicken breasts in 2 large baking dishes and rub them all over with the salt mixture. Cover and refrigerate for 20 minutes. Rinse the chicken breasts and pat dry with the paper towels.
Light a grill. Using a damp paper towel, coat the grill with the oil. Grill the chicken breasts, skin side down, over a medium-hot fire until the skin is crisp and browned, about 7 minutes. Turn and grill until just cooked through, about 9 minutes longer.