Dice the celery and onion into 1/2-inch pieces, mince the garlic clove, and cut the chicken breast into 1-inch chunks. Dice the green bell pepper and roughly chop the kale. Having everything prepped and ready before you start cooking ensures the chili comes together smoothly without scrambling mid-recipe—this is especially important when cooking for kids who are waiting to eat!
Heat the olive oil in a large pot over medium-high heat until shimmering. Add the chicken chunks and cook for 5-6 minutes, stirring occasionally, until the surface is golden and the chicken is mostly cooked through but not yet fully done. This browning step develops flavor that will carry through the entire chili. Add the diced onion and minced garlic, stirring constantly, and cook for another 3-4 minutes until the onion begins to soften and becomes fragrant.
Add the diced celery and green bell pepper to the pot and stir well, cooking for 2-3 minutes to soften slightly. Next, add the frozen corn, drained and rinsed great northern beans, chicken broth, diced green chilies, cumin, oregano, salt, and black pepper. Stir everything together thoroughly to distribute the seasonings evenly throughout the pot. I like to taste the broth at this point and adjust the seasoning if needed—it's much easier to fix now than after simmering.
Bring the chili to a boil over medium-high heat, then reduce the heat to medium-low and cover with a lid. Simmer for 25-30 minutes, stirring occasionally, until the chicken is fully cooked through and the vegetables are tender. Add the chopped kale during the last 5 minutes of simmering so it softens but retains some texture and nutrients. The long simmer allows all the flavors to meld together beautifully.
Remove the pot from heat. In a small bowl, blend or mash one of the reserved cans of great northern beans with a fork until mostly smooth, then stir this mixture back into the chili—this creates a naturally creamy texture that kids love. Pour in the milk and sour cream, stirring gently until well combined. I prefer whole milk for its richness, which makes the chili feel more indulgent without being heavy. The sour cream should be stirred in off the heat to prevent any chance of curdling.
Ladle the chili into bowls and serve warm. This white chicken chili tastes great on its own, but consider topping with shredded cheese, crushed tortilla chips, or a dollop of sour cream for added appeal to younger eaters. Leftovers keep well in the refrigerator for up to 4 days.