1. Using poultry shears or sharp knife, split the chicken along the backbone, leaving the breastbone intact, a preparation technique known as spatchcocking.
2. Flatten the chicken by pressing down on it firmly.
3. In a shallow, glass baking dish, mix together all ingredients for the marinade-1/4 cup Dijon mustard, 2 tablespoons chopped fresh parsley, 1 tablespoon minced garlic, 1/2 teaspoon salt, and 1/4 teaspoon freshly ground black pepper.
4. Add chicken, rubbing marinade over entire surface. Cover the dish with plastic wrap and refrigerate for 20 minutes or up to 1 hour.
5. While chicken is marinating, prepare coals for the grill. Grill chicken over medium-hot coals for 30 to 35 minutes, until a thermometer inserted in the thickest part of the thigh registers 170 degrees F. Discard remaining marinade.
6. While chicken is grilling, whisk together all ingredients for Warm Orange-Thyme vinaigrette in a small, glass or nonstick saucepan-olive oil, orange juice, 2 teaspoons Dijon mustard, white wine vinegar, minced fresh thyme, 1/2 teaspoon salt, and 1/4 teaspoon freshly ground black pepper.
7. Transfer the grilled chicken to a cutting board and let cool for 5 minutes. Over low heat, warm vinaigrette, whisking well.
8.Carve the chicken and pour vinaigrette into a gravy pitcher. Serve chicken warm and pass vinaigrette separately.