In a small bowl add the balsamic vinegar, honey, fresh peach juice, and a pinch of sea salt and pepper. Whisk together.
Preheat the grill to 350-400 degrees. Lightly coat the grate with avocado oil then place the chicken on the grill. Grill for 10 minutes, turn the chicken over, and grill for an additional 10 minutes or until the chicken is cooked through and has reached an internal temperature of 165 degrees. Remove from the grill, slice into 1/2" thick slices or dice into bite-size pieces and drizzle with two tablespoons of the balsamic-honey dressing over the cut pieces.
Slice the peaches in half and remove the pits. During the last 5 minutes of cooking the chicken, place the peaches, cut side down on the grill.