Boil the chickpea pasta in salted water until al dente, reserving 1/4 cup of the starchy cooking water before draining.
While the pasta cooks, dice the guanciale, pancetta, and chicken breast into small, uniform pieces.
In a cold skillet, add the guanciale and pancetta, then turn the heat to medium to render the fat until the bits are golden and crispy.
Remove the crispy meat with a slotted spoon, leaving the rendered fat in the pan, and add the diced chicken breast.
Sear the chicken until cooked through and lightly browned, then turn off the heat to prevent the eggs from scrambling later.
In a small bowl, whisk together the egg and Pecorino Romano cheese until a thick, uniform paste forms.
Add the hot, drained pasta and the crispy guanciale and pancetta back into the skillet with the chicken.
Quickly pour the egg mixture over the pasta while tossing constantly, adding the reserved pasta water one tablespoon at a time to create a glossy, creamy sauce.
Season the dish with sea salt and a generous amount of freshly cracked black pepper before serving immediately.