Season chicken with salt and pepper. In a deep saute pan or Dutch oven, heat 1/2 tablespoon oil over medium-high heat. Add chicken and cook, stirring often, until lightly browned, 2 to 3 minutes. Transfer to a plate and set aside.
Add remaining 1/2 tablespoon oil to the pan. Add bell peppers and onion; season with salt and pepper and cook, stirring often, about 3 minutes. Add chopped green chilies, garlic, chili powder, cumin, and oregano; cook stirring, until fragrant, about 1 minute. Add broth and milk to the pan and bring to a simmer, stirring. Stir in hominy, toasted tortilla strips and browned chicken. Salt and freshly ground black pepper to taste.
Reduce heat to low. Cover and simmer, stirring occasionally, until chicken is cooked through and sauce has thickened, about 20 minutes.
To serve, stir in 1/4 cup of the cilantro into chili. Taste and adjust seasonings. Ladle the chili into bowls and garnish with remaining chopped cilantro, lime wedges if desired. Served immediately with baked tortilla chips if desired.
Optional: Sprinkle on 1/4 cup light shredded cheese for an extra dairy serving.