Place the chicken breasts in the slow cooker. Add the white beans, green chiles, onion, garlic, chicken broth, cumin, oregano, salt, and black pepper.
Cover and cook on low for 6 to 7 hours until the chicken is tender and shreds easily.
Remove the chicken, shred it with two forks, and return it to the slow cooker. Stir in the cream cheese until fully melted and the chili thickens.
While the chili finishes, preheat the oven to 400 degrees and grease an 8x8 baking pan.
In a mixing bowl, whisk together the cornmeal, flour, sugar, and baking powder. Stir in the milk, egg, and melted butter until just combined.
Pour the batter into the prepared pan and bake for 20 minutes until the top is golden and a toothpick comes out clean.
Let the cornbread cool slightly before slicing. Serve warm alongside bowls of the white chicken chili.