Heat 1 teaspoon vegetable oil in a large, deep skillet over medium-high heat. Add chicken breasts and cook until browned, about 4 minutes. Reduce heat to medium, flip breasts, cover the pan, and cook until browned on the other side, about 5 minutes. Remove to a plate and allow to cool before chopping into cubes.
Return skillet to medium heat, add 1 teaspoon vegetable oil, onion, salt, and black pepper. Cook and stir until onion turns translucent, 4 to 5 minutes. Stir in garlic and cook until fragrant, about 1 minute.
Stir ancho chili powder, cumin, flour, chipotle pepper powder, and oregano into the onion mixture; cook and stir for 2 to 3 minutes. Add 1 cup of the chicken broth and stir, scraping up any brown bits off the bottom of the pan. Stir in cornmeal and bring to a simmer.
Stir in beans and 1 more cup chicken broth. Cut cooled chicken breasts into cubes, add to the chili and bring to a simmer. Add remaining cup of chicken broth, season with salt, black pepper, sugar, and cayenne pepper to taste; cook until heated through. Serve garnished with green onions, sour cream, and cilantro.