Place the chicken breasts, skin side up, on a sheet pan and rub them with olive oil. Sprinkle generously with salt and pepper.
Roast for 35-40 minutes or until chicken is cooked through. Set aside to cool.
When the chicken is cool, remove and discard the skin and bones and cut chicken into 3/4 inch pieces. Place chicken in bowl and add the mayo, tarragon, celery, 2 teaspoons salt and 1 teaspoon pepper and toss well.
To assemble, spread a little mayo on half the bread slices, top with the chicken salad and amount of mixed salad greens you prefer.
Cover with remaining slices of bread, cut in half and serve.