Heat olive oil in a large pot over medium-high heat. Add the diced onions and cook until soft and translucent. Toss in the garlic and cook for another 30 seconds to release its aroma.
Add chicken broth, green chilies, cumin, paprika, cayenne, oregano, lime juice, salt, and pepper. Stir well to combine. This step layers the flavors and sets the base for a rich chili.
Take a ladle of the drained beans and a splash of the broth, then blend until smooth. Return the purée to the pot along with the remaining whole beans and corn. This creates a creamy consistency without heavy cream.
Bring the chili to a gentle simmer for 15–30 minutes, allowing the flavors to meld. Stir in the shredded chicken and sour cream just before serving to keep the texture silky.
Check the seasoning and adjust salt, pepper, or lime juice if needed. This ensures the flavor is balanced and bright.