Add the olive oil to a large dutch oven or heavy-bottomed soup pot over medium-high heat. Once the oil is shimmering, add the diced onion and a big pinch of salt. Cook, stirring frequently, until the onions are translucent and golden in spots, about 7-10 minutes.
2 tablespoons olive oil, 2 medium yellow or white onions
Add the garlic, green chilies, cumin, oregano, and cayenne. Stir to combine and cook for an additional 2 minutes, stirring constantly, until fragrant.
5 cloves garlic, 2 cans diced green chilies, 4 teaspoons ground cumin, 1 ½ teaspoons dried oregano, ¼ to ½ teaspoon cayenne pepper
Add the chicken stock, beans (including the juice from the undrained beans), and the chicken. Stir to combine. Bring to a boil, then reduce the heat to medium low and simmer for about 10 minutes.
Turn the heat to low. Add the cheese a handful at a time, stirring until melted and well combined. Taste and season with additional salt and pepper as needed.
8 ounces shredded monterey jack cheese, Salt and pepper to taste
Serve garnished with sour cream, tortilla strips, sliced green onions, and/or additional shredded cheese as desired.
Notes
I like to use low-sodium chicken stock and beans when possible to better control the seasoning of the final chili. How much salt you need to add to the soup will depend on the chicken stock and beans that you use, so be sure to taste it before serving and season appropriately.
For a spicier chili, add more cayenne and/or use medium or hot diced green chilies.