Preheat oven to 400°F.
Add all of the vinaigrette ingredients into a small jar. Place the lid on and then shake the jar vigorously, until well combined.
Place the chicken and potatoes in a large bowl. Pour ¾ of the vinaigrette over the chicken and potatoes. Use a couple of large spoons to stir around the chicken and potatoes until well coated. Place in the refrigerator for at least 15 minutes, or up to 12 hours (covered).
While the chicken is resting in the fridge, prep the vegetables.
Place the vegetables on a sheet pan. Pour the rest of the vinaigrette over the top of the veggies. Use your fingers, or a large spoon, to move the veggies around to get them nicely coated.
Remove the chicken from the fridge and nestle each piece into the veggies. Pour any extra dressing from the bowl all over the top. Try and get the potatoes to lay evenly across the pan. (If they are stacked too much, they won't cook evenly). Liberally sprinkle salt and pepper over the tops of the chicken.
Place the pan in the oven and bake for 30 minutes. (After about 15 minutes, remove from the pan and use a spoon to move the veggies around somewhat).
Remove the pan from the oven and sprinkle the olives over the top. Return to the oven for another 10 minutes.
If you want the skin to be extra crispy, keep the pan on the middle rack and turn your broiler onto HIGH for about 1 to 2 minutes. Keep an eye on the chicken, don't let it burn!
Remove from chicken and sprinkle the feta and parsley all over the top. Serve at once.