Place the chicken breasts on a sheet pan and rub the skin with olive oil. Sprinkle liberally with salt and pepper. Roast for 35 to 40 minutes, until the chicken is just cooked. Set aside until cool enough to handle. Remove the meat from the bones, discard the skin, and dice the chicken in large bite-size pieces.
Meanwhile, add the broccoli florets to a large pot of salted boiling water. Cook for 1 minute, until crisp tender, drain, and place into a bowl of ice water until cool. This will stop the cooking and set the bright green color.
For the dressing, whisk together the mayonnaise, wine, mustards, 1 tablespoon salt and 1/2 teaspoon pepper. Add enough sauce to the warm chicken to moisten well. Add the tarragon, broccoli, and tomatoes and mix gently to combine. Refrigerate for a few hours to allow the flavors to blend. Serve at room temperature.