Spray a nonstick pan with nonstick cooking spray, add 1 teaspoon of vegetable oil and heat over high heat. Add chicken until brown on all sides, about 8 minutes, turn often. Remove chicken, set aside, and carefully wipe pan clean of grease and flour.
Lower heat to medium, add remaining teaspoon of oil, and cook the garlic, onions, carrots, and celery. Cook until soft, about 5 minutes.
Mash 1/2 cup of beans and add to pan with remaining can of beans, tomatoes, broth, basil, and oregano.
Bring to a boil, lower heat to medium low, and add chicken. Cover and cook until chicken is thoroughly cooked, about 30 minutes, stirring occasionally.