In a medium bowl, combine olive oil, garlic, lemon juice, salt and pepper. Add chicken breasts and coat with the marinade. Cover and refrigerate for at least 2 hours, or overnight
Preheat grill to medium-high heat
Grill chicken breasts for 4-5 minutes per side, or until cooked through.
Meanwhile, make the balsamic-mustard glaze. In a small bowl, combine Dijon mustard, capers, parsley, olive oil, lemon juice, and balsamic vinegar.
When the chicken is done grilling, brush generously with the balsamic-mustard glaze and serve.