Preheat grill to 400 degrees. Slice peaches in half and remove pits.
Brush halved peaches all over with avocado oil, and place sliced side down on preheated grill. Let cook 3-4 minutes, moving as needed to achieve more grill marks. Flip over and cook 3-4 more minutes. Meanwhile make salad dressing.
Take peaches off the grill and assemble the salad. Place greens in bowl. Salt and pepper to taste.
Slice peaches and add to top of greens. Lay sliced chicken on top.
Add the goat cheese, then sprinkle on blackberries and chopped pistachios. Drizzle with a little salad dressing and serve with additional dressing.