Whisk the oil, 1/4 cup mint, honey, mustard, lemon zest, lemon juice, shallots, 1 teaspoon salt and 1/8 teaspoon pepper together in a medium bowl. Set aside 1/3 cup for the dressing.
Add the chicken to the remaining marinade. Toss to coat, cover the bowl and allow the chicken to marinate at room temperature for 1 hour.
Meanwhile, bring the chicken broth to a boil in a medium saucepan. Add the barley, cover and lower the heat to a simmer. Cook until the liquid has evaporated and the barley is tender, 10 to 12 minutes. Set aside to cool.
Preheat a grill pan over medium-low heat. Remove the chicken from the marinade, shaking off any excess. Sprinkle the chicken all over with 1/4 teaspoon salt and 1/8 teaspoon pepper. Grill the chicken, smooth-side down, flipping once, until cooked through and firm to the touch, 20 to 25 minutes. Remove the chicken from the grill and set aside to cool.
Stir the reserved 1/3 cup marinade and combine with the barley, grapes, walnuts, remaining 1/4 cup mint, radish and celery. Season with salt and pepper. Slice the chicken and serve over the salad.
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