Heat oil in a large stock pot over medium heat. Add onion and garlic and cook, stirring occasionally, until softened. Add chiles and bell pepper and continue cooking until vegetables are tender.
Add wine and scrape up any browned bits that have stuck to the bottom. Add tomatoes and stir to combine. Add chicken, beans, and oregano and cover with water by 1-inch. Bring to a boil, then reduce heat to a low simmer. Cook until chicken is falling off the bone, about 40 minutes, adding more water if necessary to keep chicken submerged.
Carefully remove chicken to a baking sheet and let cool slightly. When cool enough to handle remove meat from chicken and return to pot, leaving all skin and bone behind. Add cilantro, lime juice and season with salt.