Preheat a grill or grill pan to medium-high heat.
Brush both sides of the chicken breasts with the olive oil and season evenly with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Grill the chicken 5 to 7 minutes on the first side, then flip and grill another 3 to 4 minutes, or until cooked through and internal temperature reaches 165°F (74°C). Remove from heat and let rest while you finish the sauce.
Meanwhile, cook the fettuccine according to package directions in a large pot of salted boiling water; drain and keep warm.
In a saucepan over medium heat, warm the heavy cream and butter just until small bubbles appear around the edges, taking care not to boil.
Whisk in the grated Parmesan until smooth, then add the garlic powder if using and whisk until the sauce thickens, about 1–2 minutes.
Slice the rested chicken breasts thinly.
Divide the cooked pasta between plates, spoon the Alfredo sauce over the pasta, and top with sliced chicken; serve immediately.