In a large skillet, heat the oil and butter over medium heat until butter is melted. Cook the chicken breasts until no longer pink. Transfer to a plate and set aside.
In the same skillet, cook the onion and garlic until the onion is translucent. Add cayenne pepper. Mix in the chicken broth.
In a small bowl, mix together the Greek yogurt and flour. Mix into the broth until thickened. Add the salt and pepper to taste. Mix in the chicken.
Meanwhile, cook the pasta according to package directions. Mix in the sauce and serve.