In a medium bowl, whisk together balsamic vinegar, olive oil, honey, garlic, Dijon mustard, Italian seasoning, salt, and pepper until emulsified.
Place chicken breasts in a shallow dish. Pour half the marinade over them, reserving the rest. Flip to coat, cover, and refrigerate for 1–1½ hours.
When ready to cook, heat grill to medium or preheat oven to 400°F. Discard used marinade.
For grill: Cook chicken 6–8 minutes per side until internal temperature reaches 165°F. Baste with reserved marinade in the last 2 minutes. For oven: Bake 20–25 minutes on a lined sheet pan. For stovetop: Sear 5–6 minutes per side in a hot, oiled skillet, then finish in a 375°F oven for 6–8 minutes.