Cook the pasta in boiling salted water until done (according to package instructions). Place cream and cream cheese in a small saucepan. Heat over low until cream cheese is melted, and whisk until smooth.
Remove from heat. Add the Parmesan cheese, eggs, garlic powder, red pepper flakes and pepper and whisk until blended. Drain pasta (reserving 1/2 cup of hot water) and return to pot. Immediately add the white sauce and toss to coat.
The hot pasta will cook the eggs. Stir in the bacon, and add some reserved pasta water to loosen the sauce. Top with grilled chicken.