Preheat grill to medium-high heat.

Whisk together first three ingredients in a small bowl.

Split chicken in half through breastbone and backbone. Rub with sauce. When preheated, push coals to one side of grill, using tongs. Replace grill rack. Or, if using a gas grill, turn off burners on one half of the grill. Set chicken on cool side of grill not over coals or burners. Close lid, open vents to maintain fire, and cook chicken about 1 1/2 hours, turning occasionally, until a meat thermometer inserted in thickest part of thigh registers 180°F.

Serve with Tomato-Watermelon Salad. To prepare stir together all ingredients in a large bowl.