Preheat the oven to 350 degrees F.
Place the chicken breasts, skin side up, on a baking sheet 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 meat from the bones and discard the skin and bones. Cut the chicken into a 3/4-inch dice.
Meanwhile, place the pecans and walnuts on a separate sheet pan and toast in the oven for 7 to 8 minutes until golden. Set aside to cool.
For the dressing, mix together the mayonnaise, sour cream, 2 teaspoons salt and 1/2 teaspoon pepper. Fold in half the chopped tarragon leaves.
Place the diced chicken in a bowl, add the pecans, walnuts and grapes. Pour the dressing over the chicken and toss well. Sprinkle the remaining chopped tarragon leaves on top, and serve on a bed of lettuce leaves.