Step 1

Whisk 2 Tbsp. oil and next 4 ingredients in a large bowl; stir in 2 tsp. salt. Add chicken breasts; turn chicken to coat, cover, and chill overnight.

Step 2

Build a medium-low fire in a charcoal grill, or heat a gas grill to medium. Remove chicken breasts from marinade; set marinade aside. Place chicken breasts on grill, skin side up. Cover and grill, moving chicken to different spots on the rack for even cooking but without turning, until slightly charred and almost cooked through, about 20 minutes. Turn chicken. Brush orange and lemon quarters with oil and arrange around chicken breasts on grill. Continue grilling until chicken breasts are golden brown and cooked through and orange and lemon quarters are caramelized, 10-15 minutes longer.

Step 3

Meanwhile, bring marinade to a boil in a small saucepan and cook until reduced to glaze consistency (about 1/3 cup); season with salt. Transfer chicken to a platter and surround with grilled oranges and lemons for squeezing over. Spoon glaze over chicken and garnish with parsley.