This recipe is designed for rotisseries that don't sit directly over the flames. If your rotisserie does sit over the flames (or if you don't have a rotisserie), use the indirect grilling method described in the note below.
2 tablespoons (1/4 stick) butter, room temperature
2 tablespoons dried herbes de Provence (see note)
1 tablespoon coarse kosher salt
2 (3 1/2-pound) chickens
Place butter, herbes de Provence, and salt in small bowl; mash with fork until blended to thick granular paste. Starting at neck end of each chicken, carefully run fingers under skin of breasts to loosen. Starting at each side of main cavity, carefully run fingers under skin of thighs to loosen. Rub herb-seasoned butter on chicken under loosened skin and on outside of each chicken. Truss chickens by tying legs together and tying wings flush to sides. Enclose chickens in extralarge resealable plastic bags. Chill at least 6 hours. DO AHEAD Chickens can be prepared 1 day ahead. Keep refrigerated. Let chickens stand at room temperature about 30 minutes before cooking.
Remove spit from rotisserie attachment and prepare barbecue (medium-high heat). Thread chickens on spit, pushing close to center. Reattach spit to motor. Place shallow disposable foil pan(s) under chickens for drips. Close grill, inserting stem of instant-read thermometer through hole in hood of grill to monitor temperature. Maintain temperature at around 400°F by opening vents to increase heat and closing vents to reduce heat. Cook chickens until thermometer inserted into thickest part of thigh registers 170°F, about 50 minutes. Turn off grill, but do not open. Let chickens rest in covered grill 10 minutes.
Slide chickens off spit and onto platter. Cut each chicken into 6 or 8 pieces and arrange on platter.
To Grill a Whole Chicken Without a Rotisserie:
If using a charcoal grill,arrange coals on either side of a disposable aluminum baking pan, dividing coals equally. If using a three-burner gas grill, light burners on left and right, leaving center burner off. If using a two-burner gas grill, light burner on side opposite disposable pan. Insert an instant-read thermometer into top vent of grill or place oven thermometer inside grill on grate over pan. Bring temperature to 350°F to 375°F. Place chicken on grate above pan. Close grill. Adjust grill vents or heat setting as needed to maintain temperature.
This dried herb mixture can be found in the spice section of supermarkets and specialty foods stores. If unavailable, use a mix of dried thyme, basil, savory, and fennel seeds.