Whisk together Dijon mustard and white-wine vinegar in a bowl until blended.

Gradually whisk in extra-virgin olive oil until the vinaigrette is emulsified.

Brush chicken breasts and zucchini halves with half of the prepared vinaigrette.

Preheat grill or broiler to medium-high heat.

Grill or broil the chicken and zucchini until the zucchini is lightly seared and still crisp, and the chicken is cooked through.

Note that the zucchini will cook faster than the chicken; monitor closely.

Once the zucchini is cooked, slice it thinly and place it in a bowl.

Toss the sliced zucchini with the remaining vinaigrette.

Allow the grilled chicken to cool slightly after cooking.

Remove the bones and skin from the chicken, if desired.

Slice the chicken into thin slivers.

Combine the sliced chicken with the zucchini and dressing.

Season the salad to taste with salt and freshly ground black pepper.

Add shredded basil to the salad and toss to combine.

Serve the grilled chicken and zucchini salad on a bed of lettuce leaves.