Heat oil in a large skillet over medium-high heat. Season chicken breasts with salt and pepper. Place flour in a flat dish and coat each chicken piece. Fry in hot oil until browned, turning as needed. Reduced heat to medium; cover and cook for about 25 minutes or until meat is tender and juices run clear.
Remove chicken from pan; pour off all drippings except 1/4 cup. Turn heat to medium and stir in the cherries, reserving some of the cherry liquid for thickening. Stir in sugar and bring to a boil. In a dish, combine reserved cherry juice and cornstarch until smooth, then stir into pan. Cook, stirring gently, until thickened.
Add orange slices and almonds to skillet, then return chicken breasts to skillet. Spoon sauce over chicken and simmer over low heat for 10 minutes before serving. Makes 3-4 servings. Enjoy!