In Dutch oven or large saucepan, cook bacon over medium-high heat until crisp. Remove bacon from Dutch oven. Reserve drippings in Dutch oven. In small bowl, combine basil and pepper; mix well. Rub onto chicken pieces. Brown chicken in hot bacon drippings, turning to brown all sides; drain. Remove chicken from Dutch oven.
Add 3 cups of the apple cider and the ketchup to Dutch oven; blend well. Add chicken, carrots, onion and green beans. Bring to a boil. Reduce heat to low; cover and simmer 45 minutes or until chicken is fork tender and juices run clear.
In small bowl, combine flour and remaining 1/2 cup apple cider; blend well. Gradually stir into hot chicken mixture. Cook and stir until stew is thickened and bubbly. Stir in bacon. If desired, add salt and pepper to taste.