Slice chicken breasts in half lengthwise to make 4 thinner pieces. Pound to even thickness.
In a bowl, whisk Dijon mustard, balsamic vinegar, 3 tablespoons lemon juice, garlic, Italian seasoning, olive oil, 1/2 tsp salt, and 1/4 tsp pepper. Set aside 1/3 cup marinade for later use.
Add the remaining marinade and chicken to a resealable plastic bag. Seal and refrigerate for 30 minutes to 3 hours.
Clean and oil grill grates. Preheat grill to medium heat (400–450°F). Grill chicken 4–6 minutes per side or until internal temperature reaches 160°F. Brush chicken with 2 tablespoons of the reserved marinade while grilling.
Drizzle remaining marinade over chicken before serving.
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Notes
Stovetop option: Heat 2 tablespoons oil in a large skillet over high heat. Let excess marinade drip off chicken, then cook for 2–4 minutes per side until done. Remove and brush with reserved marinade.Storage: Store leftovers in an airtight container in the fridge for up to 4 days. Reheat gently on the stove.