Heat olive oil in a large pot or Dutch oven over medium heat on the stove. Add the onion to the pot and saute until softened, about 4 minutes. Add the garlic and cook, stirring, for 30 seconds.
Push the onion and garlic to the edges of the pot and place the chicken breasts in the center. Brown the chicken on both sides, 3 to 4 minutes per side.
Add all of the remaining ingredients to the pot: chicken broth, cumin, oregano, salt, cayenne pepper, white beans, diced green chiles and corn. Stir.
Bring to a simmer and then reduce the heat to medium low. Cover the pot and simmer for 20-25 minutes, or until the chicken is cooked through. (The chicken should register at least 165° F on an instant read thermometer inserted into the thickest part.)
Remove the chicken to a clean plate or cutting board and let it cool slightly. Meanwhile, use the back of a large spoon to mash a few, but not all, of the beans in the pot. This will thicken the broth slightly.
Shred the chicken and return it to the pot. Taste the chili and add more salt if needed. Serve with toppings, as desired.