Heat the olive oil and butter into a large pot over medium heat.
Add in the onion, bell pepper, poblano, and jalapeño. Sprinkle with salt and cook for about 10 minutes, stirring frequently, until the veggies have softened.
Add the spices into the pot and stir to combine. Allow the spices to cook with the veggies for a couple minutes to help release their flavors.
Add in the garlic and let it cook for about 30 seconds to a minute, until it becomes fragrant, being careful not to let it burn.
Add in the beer and green chilies. Let them cook for a few minutes.
Place the chicken on top and sprinkle with some more salt.
Add in 4 cups of the broth and place the top on the pot. Adjust the temperature to medium/low heat so that the chili is just simmering.
Let the chili cook for about 30-40 minutes or until the chicken has cooked through. Timing can depend on the thickness of the chicken.
Once the chicken is cooked, remove it from the pot and use two forks to shred the chicken into small pieces, then place the chicken back into the pot and let it cook on low for another 15-20 minutes.
Add more stock if the chili is too thick.
Stir in the sour cream and serve hot! Add salt and pepper to taste.
Add toppings of choice. I recommend fresh jalapeno since the chili isn’t overly spicy.