How to Make It
Preheat the oven to 400°F.
In a large heavy skillet, heat the oil over medium high heat until hot. Sear the chicken breasts, turning once, until golden, then transfer the skillet to the oven and bake until the chicken is cooked through, 15 to 20 minutes. Transfer the chicken to a cutting board and let stand 10 minutes. Do not clean the skillet. Slice the chicken.
Bring the cream, butter, and 1/2 teaspoon each salt and pepper to a simmer in the skillet, scraping up any browned bits. Stir in the chicken and reserve.
In a large pot of boiling salted water, cook the spaghetti until al dente. Reserve 1/2 cup of the pasta cooking water, then drain the pasta. Toss the pasta with the sauce in the skillet, the cheese and 1/4 cup of the pasta cooking water. Add more pasta cooking water for a thinner sauce, then season with salt and pepper to taste and serve.