Meanwhile, in a large pot of salted water, cook the pasta until al dente, (cooked through, but still slightly firm). Scoop out ¼ cup of the starchy cooking water and add to the pan with the chicken. When the sauce is reduced by half, add the drained pasta to the pan and toss well. Add the cream, cheese, lemon juice, and lemon zest. Mix well and cook for 1 minute more. Taste and adjust the seasonings with salt and pepper if necessary. Feel free to garnish with more lemon zest or fresh herbs when serving.