Preheat your grill on medium-high heat.
In a large bowl, mix together balsamic vinegar, olive oil, minced garlic, Italian seasoning, salt, and black pepper.
Add chicken breasts to the bowl and toss to coat them evenly with the marinade.
Cover the bowl with plastic wrap and let the chicken marinate for 10 minutes.
Take the chicken out of the marinade and discard the excess liquid.
Place the chicken breasts on the grill and cook for 5 minutes on each side.
While the chicken is cooking, wrap a brick or heavy object in aluminum foil.
After 10 minutes, take the chicken off the grill and place it on a sheet of aluminum foil.
Place the lemon slices on top of the chicken, then place the foil-wrapped brick on top of the lemons.
Return the chicken to the grill and cook for an additional 5-6 minutes, or until it reaches an internal temperature of 165°F on a meat thermometer.
Remove the chicken from the grill and let it rest for 5 minutes.
Sprinkle with fresh parsley and serve hot.