Bring a large pot of water to a boil then season with salt(see notes). Cook the penne until al dente. Reserve at least ½ cup of pasta water for later use.
In a skillet, heat 1 tablespoon of oil over medium-high heat. Cook the chorizo and stir often for 1-2 minutes, until slightly crispy. Transfer to a plate.
Add cubed chicken, season with salt and black pepper, and cook until the meat is almost done. Transfer to a plate.
Add 1 tablespoon of oil to the pan, cook the onion until soft on medium heat, about 3 minutes. Add the garlic and stir just until fragrant. Add the tomato paste, stir for 1 minute. Add sugar and stir to combine.
Add the diced tomatoes. Use a spatula to crush most of the tomato chunks and gently scrape any brown bits from the bottom of the pan to prevent burning.
Add heavy cream, oregano, and ½ cup of pasta water. Simmer for 3 minutes or until reduced and slightly thickened.
Reduce the heat to medium-low. Whisk in butter and parmesan cheese. Add the chorizo, simmer for 2 minutes or longer until the sauce is thickened and creamy to your liking and enough to cover the pasta. Add salt, black pepper, and red chili pepper flakes if needed.
Add the chicken and simmer for 1-2 minutes or until the meat is fully cooked. Add the pasta and toss to combine.