You can substitute more delicate Bibb lettuce leaves if you prefer.
Bring 6 cups water to boil in large saucepan. Add snap peas and 1 teaspoon salt and cook until slightly tender, about 2 minutes. Drain snap peas, then transfer to bowl of ice water to cool completely. Drain again, transfer to salad spinner, and spin to remove excess moisture.
Whisk mustard, lemon juice, oil, ½ teaspoon pepper, and ¼ teaspoon salt in large bowl. Stir in chicken, grapes, chives, and snap peas until combined. Season with salt and pepper to taste.
Place 1 lettuce leaf on each of 4 plates. Place 1 cup chicken salad on each lettuce leaf. Serve.
