Preheat an outdoor BBQ for high heat and lightly oil grate.
In a small bowl whisk together garlic, dried tarragon, salt, ground black pepper and olive oil.
Place each chicken breast half on a piece of foil large enough to cover the chicken. Brush chicken with the garlic mixture.
Tightly seal chicken in the foil. Cook on the prepared BBQ approximately 40 minutes.
Remove from BBQ. Discard foil and juices. Place unwrapped chicken on the BBQ. Brushing frequently with remaining garlic mixture and turning often. Continue cooking 5 to 10 minutes per side or until cooked and juices run clear.