Using your fingers, remove and discard the skin, bones, and excess fat from the chicken, placing the chicken meat in a large bowl. Tear or chop meat (you should have about 3 1/2 cups).
Add mayonnaise, celery, relish, tarragon, salt, and pepper to the bowl. Stir until thoroughly combined. Spoon onto the bread, adding a lettuce leaf to each sandwich.
Tip: If you don’t have a Panera Bread Country loaf, try Panera Bread Sourdough Rolls or thinly sliced White Whole Grain, Honey Wheat or Rye loaf.