Heat some oil in a pan over medium-high heat and season the chicken breasts with salt and pepper.
Cook the chicken for approximately 6-7 minutes per side or until they are thoroughly cooked and no longer pink in the middle.
Take them out of the pan and allow them to cool slightly before using two forks to shred the cooked chicken.
In a large pot, heat some oil over medium heat and add the chopped onion and minced garlic. Sauté until the onion turns translucent.
Add the ground cumin, dried oregano, ground coriander, and cayenne pepper, and cook for an additional minute until the mixture becomes aromatic.
Add the shredded chicken, white beans, diced green chiles, and chicken broth to the pot, stirring thoroughly to combine.
Allow the chili to simmer for about 20-25 minutes, allowing the flavors to meld together. If it thickens too much, you can add a little more chicken broth.
Stir in the sour cream and grated Monterey Jack cheese, continuing to cook for a few more minutes until the cheese has melted, and the chili becomes creamy.
Season the chili with salt and black pepper to your taste, and adjust the spiciness by adding more cayenne pepper if desired.
Serve the chili hot, garnished with fresh cilantro leaves.