Place chicken breasts in a 10-inch skillet and cover with water; bring to a boil. Reduce heat to low; cover and simmer until chicken is cooked through, about 15 minutes. Remove chicken from broth and cool to the touch; cut into 1/2-inch chunks.
Meanwhile, in a small bowl, blend mayonnaise, milk, TABASCO® Green Sauce, lime juice, and salt until smooth.
In a large bowl, combine chicken, celery, green pepper, avocado, apple, grapes, and mayonnaise mixture and mix well. Spoon salad onto a lettuce-lined platter, if desired.
Makes 4 servings.