In a large mixing bowl, whisk together the olive oil, balsamic vinegar, soy sauce, Worcestershire sauce, lemon juice, brown sugar, dried rosemary, Dijon mustard, salt, black pepper, and garlic powder until smooth and the sugar is mostly dissolved.
Reserve 1/2 cup of the marinade in a separate container for basting or finishing the chicken later.
Place the chicken breasts in a large resealable bag and pour the remaining marinade over the chicken; seal the bag and gently massage to coat all pieces evenly.
Refrigerate and marinate the chicken for at least 30 minutes and up to 24 hours (4–6 hours is ideal).
When ready to cook, preheat your grill to medium-high and lightly oil the grates.
Remove chicken from the bag, letting excess marinade drip off, and grill for about 5–6 minutes per side, basting occasionally with the reserved marinade, until the internal temperature reaches 165°F.
Transfer the cooked chicken to a plate, tent loosely with foil, and let rest at least 5 minutes before serving.
If you want a sauce, bring the reserved marinade to a rolling boil and simmer until slightly reduced before using to finish the chicken.
