In a large Dutch oven, combine onion, garlic, and ginger. Cook over medium-low heat, stirring, until dry and browned, and beginning to stick to the pot about 10 minutes. Add butter, and cook for 15 minutes. Stir in 1/4 cup water and chili powder. Cook for 15 minutes. Stir in red wine, and cook for 10 minutes more.
Remove the skin from all but the chicken wings. Using a sharp knife, slash each piece two or three times to allow the sauce to penetrate the chicken. Add the dark meat to the Dutch oven, and cook for 5 minutes. Add remaining pieces of chicken. Cook for 10 minutes. Slowly add 2 3/4 cups water, and cook until heated through, about 25 minutes. Season with salt. Remove from heat, and let rest 15 minutes.
Using a paring knife, make slits in eggs, about 1/2 inch apart. Add eggs to chicken mixture, and stir to coat. Serve immediately.