In a large pot or Dutch oven over medium heat, cook the bacon until almost completely browned. Add the onion and cook for an additional 5 minutes. Turn heat to low and add garlic; cook for 30 seconds. Remove the bacon/onion mixture to a bowl using a slotted spoon. Reserve the bacon grease. Do not wash the saucepan.
Add the green beans and enough chicken broth to cover the green beans. Add the Cajun seasoning.
Bring to a low boil. Cover and reduce to simmer. Simmer for 1 - 1 ½ hours, stirring occasionally. Drain chicken broth, return bacon/onion mixture, and heat for 1-2 minutes. Add butter, stir, and serve. If needed, season with salt and black pepper to taste.
