Cook pasta according to package directions until al dente; reserve 1/2 cup pasta water and drain.
Season chicken with salt and pepper. Heat oil in a large skillet over medium-high and brown chicken until cooked through, about 5–7 minutes; transfer to plate.
In same skillet, add onion and cook until soft, 3 minutes. Stir in garlic and sun-dried tomatoes, cook 1 minute.
Pour in chicken broth, scraping browned bits, then add cream, Parmesan, oregano, and red pepper flakes. Simmer until slightly thickened, 3–4 minutes.
Return chicken to skillet and add pasta; toss to coat, adding reserved pasta water a splash at a time to loosen sauce. Adjust seasoning and garnish with basil and more Parmesan.