Preheat an outdoor grill for medium-high heat and lightly oil the grate.
For the dressing: Whisk 4 tablespoons olive oil, balsamic vinegar, shallot, Dijon mustard, and 1/2 teaspoon salt together in a bowl until well mixed.
Brush 1 teaspoon olive oil onto cut-side of peaches.
Place peaches, cut-side down, onto grill and cook until heated through, about 4 minutes. Transfer peaches to a plate.
Brush remaining oil onto both sides of chicken breasts and season with salt.
Cook chicken on the preheated grill until no longer pink in the center, about 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Slice chicken into thin pieces and cut peaches into 1/2-inch thick pieces.
Toss arugula and dressing together in a bowl. Divide dressed arugula among plates; top with peaches and chicken.
Nutritional Facts
Per 6 servings
Calories: 210
Carbohydrate: 6g
Fat: 13g
Fiber: 0g
Protein: 17g
Sugar: 5g
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