Heat the olive oil in a large pot over medium heat. Add the onions, jalapenos, and garlic, and cook until translucent and soft, about 5 minutes.
Add chicken, salt, pepper and water to the pot and cook over medium heat until tender, about 20 minutes. Remove the chicken from the water and shred.
Add half the white beans and sour cream to the pot. Use an immersion blender to blend the beans with the onions, garlic and water mixture. This will create the creamy texture for the soup.
Return the shredded chicken to the pot. Add the remaining white beans, green chilis, corn, cumin, oregano, and chili powder, and stir to combine. Bring mixture to a boil, then cover and reduce heat to low and simmer for 15 minutes. The soup will continue to thicken as it sits.
Ladle the soup into 4-6 bowls and top it with cheese, avocados, and cilantro, if desired.