Combine olive oil, lemon juice, garlic, oregano, salt, and pepper in a bowl; pour over chicken thighs in another bowl. Cover and marinate in the refrigerator for at least 30 minutes to overnight.
Preheat the oven to 375 degrees F (190 degrees C). Remove chicken from marinade and place in a roasting pan. Add potatoes.
Bake in the preheated oven for 30 minutes. Turn chicken over and baste with marinade. Bake until chicken is no longer pink at the bone and the juices run clear, about 35 minutes more. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Transfer chicken and potatoes to a serving platter and sprinkle with lemon zest.