In a 4-quart saucepan over medium heat, warm olive oil and swirl to coat pan. Add chorizo and sauté, stirring constantly and using the side of a spatula to break up chunks, until cooked through, about 3 minutes. Add onion, chiles, and tomatoes and sauté, stirring frequently, until onions soften, about 3 minutes. Turn heat to medium-low and add both cheeses, stirring constantly, until cheeses melt, about 2 minutes. Add cream and stir until heated through.
Transfer to a fondue pot set over an alcohol or sterno flame. Serve with tortilla chips, corn chips, crusty hard peasant bread cut into 1-inch cubes, potato or yuca chips, taro root chips, pita chips and/or other "dippables" of your choice.
Note: Dip can be prepared 1 day in advance. Let mixture cool, transfer it to a covered container and refrigerate. Reheat in a saucepan over low heat and transfer to a fondue pot for serving.