Marinate the chicken: Combine all of the marinade ingredients except for the chicken in a bowl or Ziploc bag. Add the chicken breasts and coat them in the marinade. Cover or seal and refrigerate for 1-3 hours.
Prep the potatoes: Quarter the potatoes into wedges. Place them in a medium sized baking dish or roasting pan (I used a 8x11 inch glass dish). Combine the remaining ingredients in a medium sized bowl and pour over the potatoes. Toss to coat.
Shake off the excess marinade from the chicken breasts and nestle them into the prepared potatoes. Bake uncovered for 1 hour, or until the chicken reaches an internal temperature of 165°F, flipping the potato wedges halfway through cooking.
Serve with lemon wedges and fresh oregano if desired.