1. Start a fire in a charcoal grill, or pre-heat a gas grill.
2. Combine garlic, oregano, olive oil, lemon juice, balsamic vinegar, salt and pepper in a medium bowl and wisk together well to make Salmoriglio mixture.
3. Season chicken with salt & pepper and cook on a medium-hot grill turning occasionally until done, about 25 minutes.
4. While chicken is cooking heat up a large saute pan, either on the other side of the grill or on the stove.
5. When chicken is cooked transfer to saute pan, pour Salmoriglio over and cook on top of grill, turning the chicken in the pan for 1 to 2 minutes.
6. Transfer chicken to serving bowl, pour Salmoriglio mixture from saute pan on top and serve.