Heat vegetable oil in skillet. Salt and pepper the boneless skinless chicken breasts. Fry chicken in the heated oil until fully cooked. Take chicken out of the pan and set aside, covered.
On medium heat, using a whisk, stir flour into the heated oil to make a roux. Over the heat, stir in the evaporated milk. Keep stirring until thick and bubbly. When thickened stir in the crumbled feta cheese (add more if you like). The feta is fairly salty, but salt and pepper the gravy to taste. If the gravy seems too thick, stir in some more milk.
Serve prepared Chicken with Feta Sauce over top. Garnish with minced chives.
This dish goes well with steamed rice or mashed potatoes and a green vegetable. The feta gravy goes well with steamed broccoli (pictured).