Preheat oven to 375. Coat chicken with oil and arrange skin side up on a roasting pan. Sprinkle chicken with lemon juice, oregano, salt and pepper. Top each piece with a piece of butter.
Cook chicken until just done (165 degrees), about 30 minutes for breasts and 40 minutes for leg quarters. Remove from oven, and top chicken pieces with feta. Press the cheese into chicken to make sure it stays and then baste the chicken with any pan juices.
Heat the broiler. Broil the chicken until the cheese is melted and golden brown, about 2 minutes.