Heat oil in a large saucepan or Dutch oven over medium-high heat. Add the onion and cook, stirring occasionally, until soft and translucent, about 5 minutes. Add the garlic, cumin, and oregano and cook for 30 seconds, stirring.
Add the chiles, enchilada sauce, chicken broth, beans, and bay leaves. Bring to a boil, reduce heat, cover pot, and simmer for 30–40 minutes. Add the chicken, season to taste with salt and pepper and simmer for another 5 minutes. Stir in the lime juice, remove the bay leaves and serve with garnishes of choice.