Cook pasta, reserving 1 cup of hot pasta water when you drain. Set pasta aside in a colander.
In the same pot, melt butter over medium heat. Squeeze in the juice of 3 to 4 lemons. Whisk together. Pour in cream and half-and-heat. Whisk until hot. Dump in cheese and whisk until melted. Add salt and pepper. Check consistency, adding some of the hot pasta water to loosen the sauce if needed.
Pour pasta and sauce into a large serving bowl. Sprinkle remaining basil all over the top, then add sliced chicken breasts. Serve immediately!