Cook pasta in salted water until al dente. Reserve 1 cup pasta water and drain.

Season chicken with salt and pepper. Heat olive oil and butter in a skillet and cook chicken until golden and cooked through. Remove and set aside.

In the same skillet, add garlic and cook briefly until fragrant. Pour in cream and simmer gently.

Stir in Parmesan until smooth. Return chicken and add pasta, tossing with pasta water as needed.