Season chicken breasts with salt and pepper, then cook them in olive oil in a large skillet over medium-high heat until golden brown and cooked through; set aside and slice into strips.

Cook fettuccine according to package directions in a large pot of salted boiling water until al dente; drain and set aside, reserving 1/2 cup of pasta water.

In the same skillet, melt butter over medium heat, then add minced garlic and cook for 1 minute until fragrant.

Pour in heavy cream and bring to a gentle simmer, then gradually whisk in grated Parmesan cheese until the sauce is smooth and thickened.

Add cooked fettuccine and sliced chicken to the sauce, tossing to coat; if needed, use reserved pasta water to reach desired consistency, and serve immediately.