Bring a large pot of salted water to a boil and cook the fettuccine according to the package instructions; drain and keep warm.
Heat 2 tbsp vegetable oil in a large frying pan over medium heat until shimmering, about 1–2 minutes.
Add 1 tbsp minced garlic and 1 tsp dried thyme to the pan and stir until fragrant, about 1 minute.
Add the chicken breast bits to the pan; season with salt and black pepper. Cook, stirring frequently, until the chicken is cooked through and no longer pink, about 6–10 minutes depending on size. Transfer chicken to a plate and set aside.
In a medium saucepan over medium heat, combine the 8 oz cream cheese, 1 stick butter, 1 cup grated Parmesan, and 1 cup whole milk. Stir continuously until the cheeses melt and the mixture begins to bubble, taking care not to scorch.
Remove the sauce from heat and stir the cooked chicken into the sauce until evenly coated.
Serve by portioning the cooked fettuccine onto plates and spooning the chicken Alfredo sauce over each portion.
