1. Season the flour with salt and pepper.
2. Dredge the chicken pieces in the flour, tapping off any excess.
3. Heat the oil in a large, deep, wide skillet or Dutch oven over a high flame and brown the chicken pieces, turning on all sides to cook evenly.
4. Remove the chicken from the skillet with a slotted spoon and set aside.
5. Lower the heat and add the onions. Stir until wilted, about 8 minutes.
6. Add the chicken pieces back to the pot.
7. Pour in the tomatoes, salt and pepper and enough water to come about three-quarters up the way of the chicken pieces. Cover and simmer over low heat for about 35 minutes.
8. Add the olives and the vinegar.
9. Sprinkle the feta into the pot, cover, and continue to cook slowly for another 10-15 minutes, or until the feta has melted and the chicken is so tender it is nearly falling off the bone. Remove and serve.
