In a medium bowl stir together oil, tarragon, pepper, salt, and garlic. Add tomatoes and shallots; toss gently to coat. Using a slotted spoon, remove tomatoes and shallots from bowl, reserving the oil mixture.
If desired, remove skin from chicken. Arrange chicken in a single layer in a shallow roasting pan. Brush with the reserved oil mixture.
Roast chicken in a 375 degree F oven for 20 minutes. Add the shallots; roast for 15 minutes. Add the tomatoes; roast for 10 to 12 minutes more or until chicken is no longer pink (170 degree F for breasts; 180 degree F for thighs and drumsticks) and vegetables are tender. Makes 6 servings.