Whisk together the marinade ingredients and pour over chicken, and refrigerate for 1 hour.
Meanwhile, cook peas in a large pot of boiling water until just tender, 2 to 3 minutes. Drain, and submerge in ice water to stop the cooking and retain color.
Preheat the grill to medium-high heat or set up grill for indirect heat. Remove chicken from marinade, and grill chicken, turning often, until internal temperature reaches 350° F, 15 to 20 minutes for drumsticks and 20 to 25 minutes for breasts. Let cool, and refrigerate until ready to serve. Just before serving, cut chicken breasts into thick slices.
Whisk together dressing ingredients. Arrange lettuce, whole mint leaves, and peas on a large serving platter. Toss chicken in dressing, and arrange on salad. Pour remaining dressing over salad.