Trim excess fat from chicken breasts. Cover breasts with plastic wrap or a plastic bag and use a mallet or other tool to pound the chicken to even thickness, about 3/4".
Place the breasts into a one gallon leakproof plastic bag. Mix 2 cups of water and 2 tablespoons of salt in a measuring cup and stir to dissolve. Pour this into the plastic bag and seal it tight. Refrigerate for at least 30 minutes or up to 2 hours.
Pre-heat your grill.
Remove the breasts from the brine and give them a quick rinse under cold water. Dry the breasts thoroughly with paper towels. Place the breasts on a plate and coat both sides with olive oil, black pepper, and Italian seasoning.
Grill the breasts on medium temperature with a gas grill or medium low temperature charcoal grill. Grill for 4 to 5 minutes per side or until the internal temperature is 150°. Remove from the grill to a clean plate and cover with foil for 5 to 10 minutes to rest.
Serve topped with the salsa and drizzled with balsamic vinegar.