Preheat oven to 450. Process the first 6 ingredients in a food processor until finely minced. With the motor running, add the oil through the tube, and process to a coarse paste. Season with salt and pepper.
Oil a large baking sheet. Pat the chicken dry and sprinkle with salt and pepper on both sides. Spread the pesto over the chicken, coating both sides. Arrange chicken, skin side up on the baking sheet. Bake chicken until tender about 30 minutes or until chicken reaches 165°f.
Notes
Chicken - can use chicken thighs, legs, or a whole chicken cut up. You might need to adjust the time.In place of tarragon, you can use basil, sage, or mint.