Combine 1 cup water, rind, and tarragon sprigs in a small saucepan. Bring to a boil; remove from heat. Place in a large bowl; cool to room temperature. Add remaining 6 cups water, salt, and sugar, stirring until salt and sugar dissolve. Place salt mixture in a 2-gallon zip-top plastic bag. Add the ice and chicken; seal. Refrigerate 3 hours, turning bag occasionally. Remove chicken from bag; discard brine. Pat chicken dry with paper towels.
Prepare grill for indirect grilling, heating one side to medium and leaving one side with no heat.
Sprinkle cavity of chicken with 1 1/2 teaspoons chopped tarragon and 1 teaspoon pepper. Lightly coat outside of chicken with cooking spray. Rub the remaining 1 1/2 teaspoons chopped tarragon and 1 teaspoon pepper evenly over outside of chicken. Place chicken on grill rack coated with cooking spray over unheated side. Close lid; grill 15 minutes. Brush chicken with 2 tablespoons lemon juice. Close lid; grill an additional 30 minutes. Brush with remaining lemon juice. Close lid; grill 15 minutes or until thermometer inserted into meaty part of thigh registers 180°.
Place chicken on a platter; cover with foil. Let stand for 15 minutes. Discard the skin.