Place the chicken breasts in a shallow non-aluminum pan. In a non-aluminum bowl, combine all the ingredients for the marinade. Pour the marinade over the chicken breasts. Cover and refrigerate for 6 hours, turning the breasts at least once.

Prepare the fire. When the charcoal or wood glows a dusty red, place the breasts, skin side down, on the grill. Grill on one side for about 10 minutes. Turn breasts over and grill for about 15 minutes, or until cooked through, do not overcook. Remove from the heat and set aside to cool for 30 minutes (but do not refrigerate).

Mix the dressing, cover and reserve.

Meanwhile, compose the salad: Remove the chicken from the bone with a sharp slicing knife. Cut into long, thin, slices including the skin. Place the shredded lettuce in a large bowl. Arrange the tomatoes, chiles, nuts, and chicken attractively over the lettuce. Peel the avocados and slice into long, thin, strips. Add the dressing and toss the salad at the table, or each ingredient may be placed individually on chilled plates, with the dressing served on the side.