Boil a large pot of salted water and cook pasta until al dente; reserve one half cup of pasta water before draining.
Heat olive oil and one tablespoon of butter in a large skillet over medium-high heat.
Season chicken strips with salt and pepper and sear until golden brown and cooked through; remove chicken from skillet and set aside.
In the same skillet, add the remaining butter and minced garlic, sautéing until fragrant.
Pour in the heavy cream and bring to a gentle simmer, scraping up any browned bits from the chicken.
Stir in the room-temperature parmesan cheese until melted and smooth.
Return the chicken to the skillet, toss in the cooked fettuccine, and add a splash of reserved pasta water if needed to adjust consistency.
Season with additional salt and pepper as desired before serving.