Sauté the diced onion in the large soup pot over medium heat until it becomes translucent and fragrant, about 5 minutes.
Add the minced garlic and cook for another minute, stirring constantly until it smells fragrant but not browned, about 30 seconds.
Pour in the chicken broth and bring it to a gentle simmer. Add the cumin and oregano, stirring to combine the spices evenly into the broth.
Introduce the chicken pieces to the broth, then cover the pot and simmer for about 15 minutes, or until the chicken is cooked through and tender.
Remove the chicken from the pot and shred it with two forks, then return it to the soup. Stir in the drained white beans and continue simmering uncovered for another 10 minutes, allowing flavors to meld.
Add the sour cream to the soup, stirring well to create a creamy texture that balances the spices. Season with salt and pepper to taste, adjusting as needed.
Simmer for a few more minutes until the soup is heated through and the flavors are well combined. The chili should be creamy and thickened, with tender chicken chunks and white beans throughout.
Ladle the hot white chicken chili into bowls, then garnish with fresh cilantro leaves and a squeeze of lime juice for brightness.
Serve immediately with your favorite bread or tortilla chips, enjoying the warm, comforting flavors and creamy texture.