In a large pot of boiling salted water, cook the fettuccine until al dente.
Meanwhile, in a large, deep skillet, cook the pancetta and bacon over moderately high heat until crisp, about 6 minutes. Add the cinnamon and cook for 10 seconds. Reduce the heat to low.
In a medium bowl, whisk the cream with the grated cheese and egg yolks and season with salt and pepper. Add the mixture to the skillet and remove from the heat.
Drain the pasta, reserving 1/2 cup of the water. Add the pasta and the reserved water to the skillet and simmer gently, tossing until the pasta is coated with a thick sauce, 2 to 3 minutes. Serve the carbonara in shallow bowls, sprinkled with the chives.