In a large pan, heat the olive oil over medium-high heat. Season the chicken with salt and pepper, then cook, stirring as needed until golden brown, 4 minutes. Add the cream, lemon zest, garlic and pepper flakes, and bring to a simmer. Cook until reduced by half. Meanwhile, in a large pot of boiling salted water, cook the fettuccine until al dente, Drain, reserving ¼ cup of pasta water, and add to the pan, along with the grated Parmesan and the butter. Toss the pasta until well coated, then season with salt and pepper. Transfer to a platter and garnish with chopped parsley, then serve.