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Season the chicken lightly with salt and pepper.
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Heat the olive oil in a large heavy skillet or Dutch oven over medium flame. Sear the chicken, in batches if necessary, turning with kitchen tongs to brown. Remove and set aside.
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Skim the excess rendered chicken fat from the skillet.
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Place onions in the skillet and cook over medium heat until translucent, about 8 to 10 minutes. Stir in the garlic.
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Add browned chicken back to pan. Pour tomatoes over mixture and add ½ cup wine or water.
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Cover and simmer for 35 - 40 minutes over medium to low heat, until chicken is almost cooked and sauce and pan juices are reduced and thickened.
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While the chicken is simmering, bring a large pot of cold water to a rolling boil, salt generously, and cook the noodles. Strain and stir gently with 3 tablespoons of olive oil. Set aside, covered, to keep warm.
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About ten minutes before removing the chicken from heat, add the oregano, olives and vinegar. Season to taste with a little salt and pepper, but judiciously since the feta will also add saltiness to the final dish.
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Sprinkle or strew the feta over the chicken and sauce. Simmer another 5 to 8 minutes, until cheese has melted. Serve hot over Greek-style noodles.