- Whisk together mustard, 1 tablespoon orange juice, orange zest, 3 tablespoons olive oil, tarragon, 1/4 teaspoon sugar, 1/4 teaspoon salt, and 1/4 teaspoon pepper in small bowl; set aside.
- Whisk together remaining tablespoon orange juice, remaining 3 tablespoons olive oil, remaining teaspoon sugar, 1 1/2 teaspoons salt, 1/2 teaspoon pepper, garlic, and water in medium bowl. Place marinade and chicken in gallon-size zipper-lock bag and toss to coat; press out as much air as possible and seal bag. Refrigerate 30 minutes, flipping bag after 15 minutes.
- Turn all burners to high and heat with lid down until very hot, about 15 minutes. Scrape grate clean with grill brush. Dip wad of paper towels in oil; holding wad with tongs, wipe cooking grate. Leave primary burner on high and turn off other burner(s).
- Remove chicken from bag, allowing excess marinade to drip off. Place chicken on cooler side of grill, smooth-side down, with thicker side facing lit burner. Cover and cook until bottom of chicken just begins to develop light grill marks and is no longer translucent, 6 to 9 minutes. Using tongs, flip chicken and rotate so that thinner side faces lit burner. Cover and continue to cook until chicken is opaque and firm to touch and instant-read thermometer inserted into thickest part of chicken registers 140 degrees, 6 to 9 minutes longer.
- Move chicken to hotter side of grill and cook, uncovered, until dark grill marks appear, 2 to 3 minutes. Using tongs, flip chicken and cook until dark grill marks appear and instant-read thermometer inserted into thickest part of chicken registers 160 degrees, 2 to 3 minutes longer. Transfer chicken to cutting board, let rest, tented with foil, 5 minutes. Slice each breast on bias into 1/4-inch-thick slices and transfer to individual plates. Drizzle with reserved sauce and serve.
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