Whisk olive oil, lemon juice, oregano, garlic, rosemary, and tarragon together in a measuring cup.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Place chicken on a rimmed baking sheet. Pour 1/2 of the oil mixture over the chicken and reserve the remaining 1/2. Using your hands, massage the oil mixture into the chicken skin. Season with salt and pepper.
Grill chicken skin-side up over indirect heat for 50 minutes. Move chicken over direct heat and grill 5 minutes. Carefully flip chicken over skin-side down and grill until skin is brown and crispy, about 5 more minutes. Transfer chicken to a serving platter and let rest for 10 minutes.
Drizzle reserved oil mixture over the chicken. Carve and serve.