This chili is good the day it's made and even better reheated the next day for lunch. We use dark chicken meat rather than white, so it will remain tender.
In a large pot (5 quarts), warm oil over medium-high heat. Brown chicken until golden, 3 to 4 minutes per side. Transfer to a plate; set aside.
Reduce heat to medium. Add onion, garlic, and chile; cook, stirring often, until onion softens, 3 to 4 minutes.
Cut browned chicken into 1/2-inch strips. Add chicken, broth, and beans to pot; bring to a boil. Reduce heat to an active simmer, and cook until chicken is very tender and chili has thickened, 25 to 30 minutes.
Reserve 1/2 cup hominy to use as garnish; stir remaining hominy into chili. Season with salt and pepper. Ladle into bowls; garnish each serving with reserved hominy and cilantro, and drizzle with jalapeno sauce, as desired.
If you like your chili spicy, substitute hot chicken sausage for the dark chicken meat.