Heat the oil in a large saucepan over medium heat. Add the onion and garlic; sauté, stirring occasionally, until tender, for about 5 minutes. Increase the heat to medium-high.
Add the ground turkey; cook, stirring frequently, until browned, about 4 minutes. Add the chili powder, oregano, black pepper and hot red pepper; cook, stirring, for 30 seconds. Add the tomatoes, tomato sauce and water. Reduce the heat and simmer, covered, for about 30 minutes.
Meanwhile, cook the rice following package directions. Keep warm.
Stir the black beans, cannellini beans and vinegar into the chili. Cook over medium heat, stirring occasionally, until the chili is heated through.
Spoon the chili over the warm rice on a large serving platter or on individual dinner plates. Makes 6 servings.