Preheat oven to 375 degrees F. In a medium bowl combine oil, tarragon, garlic, salt, and pepper. Add tomatoes; toss gently to coat. Using a slotted spoon, transfer tomatoes to another bowl, reserving oil mixture. Add onions to oil mixture; toss gently to coat. Using the slotted spoon, transfer onions to another bowl, reserving oil mixture.
Arrange chicken in a shallow roasting pan. Brush chicken with the reserved oil mixture. Add onions to roasting pan.
Roast chicken and onions for 35 minutes. Add tomatoes; roast about 10 minutes more or until chicken is done (170 degrees F for breasts; at least 175 degrees F for thighs and drumsticks) and vegetables are tender.