Place the pancetta in a single layer in a large, cold skillet. Cook over medium heat, stirring occasionally, until the pancetta turns golden brown, becomes crispy, and the fat renders, about 8 to 10 minutes. Use a slotted spoon to transfer the pancetta to paper towels to drain.

Season the chicken with 1/2 teaspoon of salt on all sides. In the same skillet, cook the chicken over medium heat, turning occasionally, until golden brown on both sides and an instant-read thermometer inserted into the thickest part reads 165°F, about 12 to 15 minutes. Transfer the chicken to a cutting board and let it rest for a few minutes before chopping it into bite-sized pieces.

In a large, heatproof bowl, whisk together the egg yolks, whole egg, and Pecorino Romano. Season with freshly ground black pepper.

Fill a large pot with 8 cups of water and generously salt it. Bring the water to a boil, then cook the pasta, stirring occasionally, until al dente, following the package directions. Using a slotted spoon, quickly transfer the hot pasta to the egg mixture, tossing continuously until the pasta is evenly coated and the sauce becomes smooth and glossy. Gently fold in the pancetta and chicken. Adjust the seasoning with more salt, if needed.