Heat olive oil in a large pot over medium-high heat. Add chopped onion and sauté until softened, about 3–5 minutes. Add minced garlic and cook for an additional 30 seconds.
Pour in the low-sodium chicken broth along with canned diced green chilies, ground cumin, cayenne pepper, paprika, dried oregano, lime juice, salt, and pepper to taste. Stir well to combine.
Drain and rinse the great northern beans using a strainer.
Measure out a big ladleful of the rinsed beans and place them in a food processor with a splash of broth from the soup. Puree until smooth.
Add both pureed and whole beans back into the pot along with corn. Bring everything to a simmer and let it cook uncovered for about 15 to 30 minutes.
Remove from heat and stir in sour cream along with your cooked shredded chicken.
Serve your White Chicken Chili garnished with fresh cilantro, shredded cheese, avocado slices, and tortilla chips if desired.