Cook the Aromatics:
Heat olive oil in a large pot over medium heat. Add the onion and cook until softened, about 3–4 minutes. Stir in the garlic and cook for another 30 seconds until fragrant.
Cook the Chicken:
Add the chicken breasts to the pot, then pour in the chicken broth. Bring to a boil, reduce to a simmer, and cook until the chicken is fully cooked and tender, about 15–20 minutes.
Shred the Chicken:
Remove the chicken from the pot and shred it using two forks. Set aside.
Build the Chili:
Return the shredded chicken to the pot. Add the white beans, green chiles, cumin, chili powder, oregano, smoked paprika, salt, and pepper. Stir well to combine.
Simmer the Chili:
Simmer the chili over medium-low heat for 15–20 minutes, allowing the flavors to meld.
Add the Creaminess:
Stir in the sour cream, heavy cream (if using), and lime juice. Mix until the chili is creamy and heated through.
Serve:
Ladle the chili into bowls and garnish with fresh cilantro, shredded cheese, avocado slices, or crushed tortilla chips, if desired.