Preheat your grill to medium-high heat. Brush with oil and then season the chicken breasts with salt and pepper. Grill 5 to 7 minutes on the first side and then flip the chicken over and grill for another 3 to 4 minutes, or until cooked through.
Prepare the Alfredo sauce by combining the cream and butter in a saucepan over medium-high heat. Do not let the mixture come to a boil, but heat until small bubbles begin to form. Add the Parmesan cheese and whisk quickly. Add the garlic powder and continue to whisk. The sauce will thicken after a minute or two.
Cut the chicken breasts into strips. Serve by placing half the pasta on each plate, then topping it with sauce and a sliced chicken breast.