Heat the olive oil in a large skillet over medium heat.
Add the chicken and brown on all sides. Remove chicken with a slotted spoon and set aside. In the same skillet, add the onion, carrot and bell pepper. Cook and stir until soft, about 8 minutes. Add the garlic and cook for 1 minute longer.
Pour in the heavy cream. Stir in the tomato, tomato paste and Parmesan. Add the basil and sugar. Bring the mixture to a boil. Season with cayenne, salt and pepper, to taste. Add the chicken and reduce heat to low. Cover and cook until the chicken is cooked through, about 10 minutes.
Once chicken is cooked through, stir in the Gemelli pasta.