Prepare the compound butter: Using a fine zester, grate the zest off the lemons, grapefruit and orange. Reserve the citrus for the marinade. Add the zest to a mixing bowl with the butter, Fresno chile, minced shallot, chives, 1 teaspoon salt and a sprinkle of freshly ground black pepper. Mix together well and set aside.
Marinate the chicken: Slice the citrus into 1/4-inch rounds and add to a large baking dish with the garlic, orange juice, olive oil, Dijon, vinegar, 1 teaspoon salt and 1/2 teaspoon freshly ground black pepper. Mix well to combine. Add the chicken breasts and toss well to coat, using your hands or tongs to squash the citrus and massage it into the chicken. Cover and refrigerate for 45 minutes.
Heat a grill to medium-high. Preheat the oven to 350 degrees F.
Remove the chicken from the fridge and allow to come to room temperature. Remove from the marinade and discard. Season the breasts on both sides with salt and 4 to 5 turns of freshly ground black pepper. Place the chicken skin-side down on the grill, and cook for about 2 minutes. Rotate 90 degrees and cook for another 2 minutes; this creates nice cross-hatch sear marks on the chicken. Turn the chicken breasts over and repeat the same cooking process on the second side.
Once the chicken is marked off, place it on a baking sheet skin-side up. Brush the top of the chicken liberally with the citrus compound butter. Finish cooking in the oven until cooked through, 20 to 25 minutes. Allow to rest for 4 to 5 minutes. Slice the breasts by removing the meat from the bone and cutting into thick slices (or serve whole individual portions). Top with a small spoonful of remaining compound butter so it melts into chicken as it is served.