Heat oil over medium-high temperature in a large, heavy stockpot. Add chicken thighs, skin side down, and brown.
Add 2 cups of the broth to pan and turn heat down to medium-low. Cover pot with lid. Cook about 40 minutes, until chicken is cooked through. Leaving broth in pan, remove chicken to a bowl and set aside to cool slightly. Cover and refrigerate.
Add remaining broth to pan. Stir in remaining ingredients (except salt, pepper and parsley). Bring to a boil, reduce heat to low and cover pan. Simmer about 1 1/2 hours, until barley and vegetables are done.
Meanwhile, remove chicken meat and skin from bones. Discard bones and coarsely chop meat and skin (if you do not want the skin, skip the browning process and discard skin after removing meat from bones). Add to pot for last 1/2 hour and cook until heated through. (If soup is too thick at this point, add some water) Add salt and pepper to taste.