Preheat oven to 400º F.
Heat a dutch oven or cast iron braiser over medium-high heat. Add olive oil, then add 3 chicken thighs, skin-side down. Allow the skin of the thighs to brown well, pressing down to evenly cook the skin. Remove from the pan, and repeat with remaining chicken thighs. Do not overcrowd the pan, which will cause them to overcook before they begin to brown.
Drain most of the fat out of the skillet. Add the onions and green peppers, and sauté over medium high heat for about 10 minutes until softened.
Add the rice and chicken broth into the vegetable mixture, and bring the broth to a boil.
Turn off the burner, and nestle the chicken breasts on the top of the rice mixture. Cover the pan with the lid.
Transfer the cast iron pan to the oven and bake for 30 minutes, until rice is cooked.
Sprinkle the olives, cherry tomatoes, and feta cheese over the chicken and rice. Add the lemon slices to the top of the dish.
Return to the oven, uncovered, and continue baking for an additional 10 minutes.
Garnish with chopped Italian parsley prior to serving, if desired.