In a food processor, blend butter, rosemary, garlic, lemon zest, and lemon juice together. Pour 1/3 of the blended mixture into a small bowl for marinade. Cover remaining mixture, and set aside.

Lightly season chicken breasts with salt and pepper. Rub chicken breasts with marinade. Place chicken breasts on a platter, cover, and refrigerate for 3 hours.

Preheat an outdoor grill for high heat and lightly oil the grate. Transfer half of the reserved rosemary and lemon mixture into a bowl for basting. Cover remaining mixture, and set aside for topping cooked chicken.

Cook chicken breasts on hot grill, basting with rosemary and lemon basting mixture, about 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove chicken breasts from the grill, and top with remaining rosemary and lemon mixture.