In a shallow bowl, whisk together 1/4 cup balsamic vinegar, 2 tablespoons olive oil, 2 tablespoons brown sugar or honey, 2 minced garlic cloves, 1 teaspoon dried Italian seasoning, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until smooth.
Add the 4 medium boneless skinless chicken breasts to the marinade and turn to coat both sides; cover and refrigerate for at least 30 minutes or up to 4 hours.
Preheat the grill to medium-high heat.
Remove the chicken from the marinade and discard any excess liquid.
Grill the chicken 6–7 minutes per side, flipping once, until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Transfer the chicken to a plate and let rest for 5 minutes before serving.