Heat oven to 325 degrees. Season the chicken breasts with 1 teaspoon of the salt and 1/2 teaspoon of pepper. Drizzle breasts with vegetable oil to coat completely
Place in a 9-by-13-inch glass baking dish. Transfer to oven, and bake until the flesh is firm and the juices run clear when pierced with a two-pronged fork, 60 to 75 minutes
Remove from oven, and let the chicken cool completely, about 20 minutes. Remove, and discard the skin
Remove meat from bone in one piece, or in as large pieces as possible. Discard the bones, or reserve them to use for stock
Cut chicken into large bite-size pieces, and place in a medium size bowl. Add mayonnaise, tarragon, salt, and pepper. Stir well to combine without breaking up the chicken
Using a bread knife, slice 8 1/2-inch thick slices of bread. You can slice bread in the regular manner, or slice the long way, creating 8 very large 1/2-inch thick slices
Cover 4 slices of bread with Bibb lettuce, and mound chicken on top. Cover with remaining slices of bread, and serve.
