In a separate large skillet, heat 2 tablespoons of vegetable oil over medium-high heat. Add the diced onion and cook until slightly softened. Add in garlic, chili powder, oregano and cumin. Stir and cook until fragrant, about 1 minute. Add the shredded, cooked chicken. Season with salt and pepper. Stir in the green chilies and continue to stir and cook mixture for another 5 minutes, or until thoroughly heated. Set aside.