In a large pot or Dutch oven, heat olive oil over medium heat. Add diced onion and sauté until soft, about 5 minutes.
Stir in minced garlic and cook for an additional minute until fragrant.
Add the chicken breasts to the pot and cook until they start to brown, about 5-7 minutes.
Stir in the diced green chilies, chicken broth, great northern beans (if using), cumin, chili powder, smoked paprika, salt, and pepper. Bring the mixture to a boil.
Reduce heat to low, cover, and let simmer for about 20 minutes, or until the chicken is cooked through.
Remove the chicken breasts from the pot. Shred the chicken using two forks and return it to the pot.
Stir in the heavy cream and let the chili simmer for an additional 5 minutes. If desired, stir in the shredded Monterey Jack cheese until melted and creamy.
Serve hot, garnished with fresh cilantro and lime wedges on the side.