Melt 3 tablespoons of butter in a large skillet over medium-high heat. Add the chicken, and cook until browned on both sides and no longer pink in the center, about 10 minutes; place into a 9x13 inch baking dish and set aside.
Reduce the heat to medium, and melt the remaining butter in the pan. Stir in the garlic, and onion, and cook for 2 minutes, stirring constantly until the onion has begun to soften. Stir in the flour, and continue cooking 5 minutes more. Add the vodka, and bring to a simmer over medium-high heat, stirring constantly. Allow to simmer for 2 minutes, then stir in the tomato paste, chicken broth, salt, pepper, parsley, sour cream, and feta cheese. Reduce heat to medium-low, and simmer 20 to 30 minutes stirring frequently.
Preheat oven to 350 degrees F (175 degrees C).
Pour the hot sauce over the chicken breasts, and bake in preheated oven until the top has browned, about 20 minutes.
