Prepare ingredients: chop 1 pound chicken breast into bite-size pieces; chop 1 medium onion; mince or press the garlic (1 clove garlic — 1 tablespoon minced as listed); chop 2 stalks celery; dice 1 medium green bell pepper; remove stems and chop 1/2 bunch kale if using; measure 1 cup frozen corn. Open the 3 cans of great northern beans and 1 can diced green chilies. Drain and rinse two of the bean cans and set them aside; reserve the remaining bean can (do not rinse) to puree later.
Heat 1 tablespoon olive oil in a large stock pot over medium heat.
Add the chopped chicken to the pot and cook, stirring occasionally, until the pieces are almost cooked through (no longer raw on the outside), about 4–6 minutes.
Add the chopped onion and the minced/pressed garlic to the pot and sauté until the onion is softened and mostly translucent, about 3–4 minutes.
Add the chopped celery, diced green bell pepper, and chopped kale (if using). Cook, stirring, until the vegetables begin to soften, about 3–5 minutes.
Add 1 cup frozen corn, the two drained and rinsed cans of great northern beans, 1 1/2 cups low-sodium chicken broth, 1 can diced green chilies, 1 teaspoon ground cumin, 1 teaspoon dried oregano, 1/2 teaspoon ground black pepper, and 1 teaspoon salt. Stir to combine.
Bring the pot to a gentle boil, then reduce the heat to low, cover, and simmer for 30 minutes.
While the chili is simmering, empty the reserved can of beans (do not rinse) into a blender or food processor and puree until smooth. Alternatively, use an immersion blender in a bowl to puree them.
After the 30-minute simmer, stir the pureed beans into the pot and simmer 2–3 more minutes to incorporate.
Remove the pot from the heat and stir in 1/2 cup milk and 1 cup sour cream (or Greek yogurt) until fully combined.
Taste and adjust seasoning if desired, then serve the white bean chicken chili hot.