Heat the oil in a large pot over medium heat. Place turkey in the pot, and cook until evenly brown. Stir in leeks, and cook until tender.
Pour water into the pot. Mix in tomatoes, chili beans, and garlic. Season chili powder, paprika, oregano, cayenne pepper, cumin, salt, and pepper. Bring to a boil. Reduce heat to low, cover, and simmer 30 minutes.