Spray v-rack with vegetable oil spray. Pat chickens dry with paper towels and prick skin all over with skewer or paring knife. Combine Sugar, salt and pepper in a small bowl, then rub seasoning mix all over the chickens. Tuck wings behind back and tie legs together with kitchen twine. Arrange chickens, breast side up, head to tail on prepared V-rack.
For Charcoal Grill
Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over grill. Set cooking grate in place, cover and open lid vent completely. Heat grill until hot, about 5 minutes.
For a Gas Grill
Turn all burners to high, cover and heat grill until hot, about 15 minutes. Turn all burners to low. (adjust primary burner as needed to maintain grill temperature around 325 degrees.)
For the Brown Sugar-Balsamic Glaze
Simmer brown sugar, balsamic and salt in a small saucepan over medium heat until thickened, 3 to 5 minutes. Warm glaze through before brushing on the chicken.
To Cook the Chickens
Arrange v-rack on cooking grate and grill, covered, until back of each chicken is well browned, about 15 minutes. Flip chickens and repeat until breasts are well browned and thighs register 155 degrees, 30 to 40 minutes longer. Brush chickens with glaze and continue grilling with lid on, flipping and glazing chickens every 5 minutes, until lightly charred in spots and breasts register 160 degrees and thighs register 175 degrees, 15 to 25 minutes.
Transfer chickens to carving board, tent with aluminum foil, and let rest for 10 minutes. Carve and drizzle chicken with remaining glaze. Serve.