Trim any extra fat from the chicken breasts and place them in a bowl or a gallon size freezer bag.
In a small bowl, whisk the olive oil, balsamic vinegars, mustard, garlic, lemon juice, herbs, salt, and pepper. Reserve half of the marinade and add the other half to the bowl or bag with the chicken. Marinate for at least thirty minutes up to overnight, turning occasionally.
When ready to grill, preheat your grill with one side on high heat and the other side off.
Oil the grill grates well and drizzle the chicken breasts with more olive oil, then place the chicken breasts on the hot grill. Cook for two to three minutes or until grill marks appear, then flip the chicken and cook for another two to three minutes.
Move the chicken to the cooler grates of the grill, cover, and cook for ten minutes. Transfer a few tablespoons of the reserved marinade to another bowl and use it to baste the chicken while flipping.
Continue cooking, basting, and flipping until the breasts have an internal temperature of 165ºF. Move the chicken to the hot side of the grill to add more grill marks and color to the breast.
Transfer the chicken to a platter and cover with aluminum foil. Let rest for five minutes. Serve with olive tapenade, chunks of feta cheese, minced herbs, and drizzle with any leftover marinade or olive oil.
Add the garlic and olive oil to the bowl of a food processor and process on high until well combined. Scrape down the sides of the bowl with a spatula, then add the sun-dried tomatoes and process until the tomatoes are chopped.
Add the green olives and the Greek olive mix, and pulse two times until coarsely chopped. Stir in lemon juice, balsamic vinegar, pepper, parsley, and capers.
This tapenade will keep refrigerated for up to two weeks.
