start by coating the chicken in the balsamic marinade ingredients. Let marinate for at least 1 hour in the fridge but overnight is better for more flavor.
when the grill is hot, add the chicken and zucchini to the grill and turn the heat down to medium. Grill until the chicken is easy to turn, and there's grill marks on the zucchini.
serve everything family style, or slice the chicken and arrange it on a plate alongside some zucchini and top with caprese salad if you're entertaining. You can also arrange it this way on a large platter.