Whisk together the oil, lemon zest and juice, vinegar, mustard, tarragon, honey, 1/4 teaspoon salt and some pepper in a medium bowl. Place the chicken in a large resealable bag and pour in half of the dressing. Seal the bag and allow the chicken to marinate in the fridge for at least an hour. Reserve the remaining dressing for the arugula.
Preheat a grill to medium high. Remove the chicken from the marinade, season with some salt and pepper and grill until cooked through, 3 to 4 minutes per side. Grill the lemon halves cut-side down until grill marks appear, about 6 minutes. Transfer the chicken and lemon to a platter.
Pour the remaining dressing over the arugula and toss to coat. To serve, place 1 chicken breast on each plate and top with the arugula, a sprinkling of Parmesan and a grilled lemon half.