1.Reserve ¼ cup of the flour. Place the remaining flour in a resealable plastic bag. Add bison chuck roast cubes, a few at a time, shaking to coat. Heat oil over medium-high in a 5- to 6- quart Dutch oven or pot. Brown bison cubes in batches on all sides in hot oil. Drain off fat. Stir in 3 cups of the broth, the cranberry juice, cranberries, onion, thyme, marjoram, sugar, salt, and pepper. Bring to boiling; reduce heat. Simmer, covered, for 1 hour.
2.Stir in green beans, carrots, and celery. Simmer, covered, for 1 more hour, or until bison and vegetables are tender. Stir the remaining ½ cup broth and the reserved ¼ cup flour in a small bowl until smooth; stir into stew. Cook and stir until thickened and bubbly; cook and stir 1 more minute.