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In a large heavy skillet or Dutch oven, slowly heat the olive oil. Place onions in the skillet and sauté until translucent and slightly colored. Transfer the onions in a bowl and set aside. Don't throw away the oil.
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Place the skillet back on the stove. Add more olive oil if needed. Dredge chicken lightly in seasoned flour. Shake off the excess flour. Brown the chicken by placing a few pieces at a time if necessary in the skillet and turning them frequently. (If there is more than one batch, set the pieces aside until all of the chicken is browned.)
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Pour tomatoes over mixture, add red wine vinegar, and tomato paste. Season with oregano. Add the onions as well. Season with salt. Cover and simmer for about 35 minutes over medium heat, until chicken is almost cooked, adding water, if necessary, to keep the meat from drying out.
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About 10 minutes before removing skillet from heat, add pitted green olives. Sprinkle crumbled feta over the chicken. Simmer another 10 minutes or so, until cheese has melted. Serve hot over rice or mashed potatoes or Greek fries.
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Note: Greek cooking offers dozens of great chicken recipes. This one, with feta and green olives, is easy and quick, and delicious. Feta, olives, tomatoes and chicken make a great combination. Potatoes fried in olive oil go great with this chicken dish. So do mashed potatoes, rice, even pasta.