Preheat the oven to 350 degrees F.
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 to 40 minutes, until the chicken is cooked through. Set aside to cool.
When the chicken is cool, remove and discard the skin and bones and cut the chicken into 3/4-inch dice. Place the chicken in a bowl and add the mayonnaise, tarragon, celery, 2 teaspoons salt, and 1 teaspoon pepper and toss well.
To assemble, spread a little mayonnaise on half the bread slices, top with the chicken salad and mesclun mix, and cover with the remaining slices of bread. Cut in half and serve.
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