Place 1 chicken breast between two pieces of plastic wrap or in a resealable plastic bag. Using a meat pounder or rolling pin, pound the chicken lightly into an even thickness. Repeat with the remaining chicken breasts.
In a large resealable bag, mix together the balsamic vinegar, lemon juice, olive oil, garlic, rosemary, basil, honey, salt and pepper. If using a bowl, whisk the ingredients to combine.
Add the chicken and toss until coated with the marinade. If using a resealable bag, gently squeeze the air out. Marinate for 30 minutes at room temperature or up to 4 hours in the refrigerator.
When ready to cook, remove the chicken from the refrigerator and allow it to come to room temperature for 15 to 30 minutes before cooking.
TO GRILL :
Preheat grill over medium-high heat to 400 to 450ºF (204 to 232ºC).
Carefully grease the cooking grates with the oil.
Keep one burner off for indirect heat cooking.
Place the chicken on the direct heat side of the grill and close the lid.
Cook each side for about 3 to 4 minutes. Flip the chicken and move it over the indirect heat side of the grill.
Cook covered until the recommended internal temperature is reached (see notes), time will depend on the thickness and type of chicken.
Remove from the grill and allow it to rest for 5 - 10 minutes before serving or slicing.
Stove top:
Grease a skillet and heat to medium-high heat. Remove chicken from the marinade and discard the marinade.
Cook the chicken for about 6 to 8 minutes, flip and cook the other side for about 3-4 minutes or until the recommended temperature is reached (See notes). Time will vary depending on the thickness and type of chicken.
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Notes
Don't marinade the chicken for more than 4 hours. The marinade contains acid (vinegar and lemon juice) which can change the texture of the chicken.
It's not necessary to prick or score the chicken breast before marinating.
After grilling or pan searing, allow the chicken to rest 5 to 10 minutes, loosely tented with foil before serving or slicing.
This balsamic chicken marinade yields about 1 cup of marinade and can be used to marinate about 2 to 2.5 pounds of chicken.