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 until cool.
When the chicken is cool, remove the meat from the bones and discard the skin and bones. Cut the chicken into a 3/4-inch dice. Place the chicken in a bowl; add the mayonnaise, tarragon leaves, celery, grapes, 1 1/2 to 2 teaspoons salt, and 1 teaspoon pepper and toss well.
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