Slice the chicken breasts in half widthwise and pound to even thickness to get 4 even pieces of chicken. Set aside in a large ziplock bag. In a medium-sized bowl, whisk together the Dijon mustard, balsamic vinegar, lemon juice, minced garlic, paprika, Italian seasoning, olive oil, and salt + pepper. Add salt and pepper to personal preference; I add 1/2 teaspoon salt and 1/4 teaspoon pepper. Whisk until ingredients are combined and then remove 1/3 cup of this mixture and set aside in the fridge.
Pour the remaining mixture over the prepared chicken breasts. Seal the bag, knead the chicken to coat in the marinade, and place in the fridge. Let chicken marinate for at least 30 minutes, up to 4 hours. (I don't recommend marinating it too much longer as the acid in the mixture starts to dry out or "cook" the chicken.)
Make sure your grill grates are clean and greased. To grease, dredge a paper towel in vegetable oil and holding it with tongs, rub it all over the grate. Preheat the grill to medium heat about 375-450 degrees F. Don't go hotter than 450 to avoid drying out the chicken. Grill the chicken until completely cooked through (about 4-6 minutes per side depending on heat of the grill) Chicken should be at 165 degrees F at its thickest part. Remove 2 tablespoons from the reserved 1/3 cup marinade. Generously brush chicken with the reserved marinade mix as it grills. Reserve those last 2 tablespoons for the finished chicken.