Set the chickens on a rimmed baking sheet, sprinkle them all over with salt and pepper, and drizzle with olive oil. Roast to an internal temperature of 160 degrees F, taken between the breast and thigh, about 1 hour.
Allow to cool. With two forks, shred all the meat off the bone.
In a large bowl, combine the shredded chicken, mayonnaise, grapes, walnuts, celery, apples, chives, lemon juice and big pinches of salt and pepper. Toss well.
To assemble the sandwiches: Fill a leaf of butter lettuce with some chicken salad. Sandwich the stuffed lettuce with two slices of bread spread with mayo. Repeat for the remaining sandwiches. Slice in half and enjoy.