Preheat large skillet over medium high heat and add 1 tablespoon butter. Season chicken with salt and pepper and add to skillet. Cook chicken until golden brown, about 8 minutes. Flip and cook until other side is brown and chicken is cooked through, another 5-8 minutes. Remove chicken from pan and let cool slightly, then slice and set aside.
Reduce heat to medium low and add remaining 1/2 cup butter and heavy cream, stirring to combine. Stir in 1 cup parmesan.
Meanwhile, cook fettuccine in large pot of salted water until al dente. Drain, reserving 1 cup of cooking liquid.
Add fettuccine and sliced chicken breast to skillet with remaining 1 cup parmesan. Toss until well coated with sauce. Add cooking liquid a little at a time if needed to loosen up the sauce. Serve immediately.