Heat the olive oil over medium-high and add the onion. Saute, stirring occasionally, until onion begins to brown, about 10 to 15 minutes. Add the garlic and jalapeno and continue cooking for 3 minutes.
Transfer the onion-garlic-jalapeno mixture to your slow cooker (I used this 6-quart slow cooker), along with the rest of the ingredients for the chili. Stir well and cover. Cook on low for 8 hours.
Use a fork to fish out the chicken breasts and place them on a cutting board. Use two forks to shred the chicken, then place it back in the crock pot. If time allows, let the chicken soak in the chili for at least 1 hour (overnight is better) for maximum flavor.
Serve heaping bowls of chili with your favorite toppings.
*I used 1 can of cannelini beans, and 1 can of Great Northern Beans