Bring a large pot of salted water to a boil and cook the whole wheat spaghetti until al dente, according to package directions.
While the pasta is boiling, dice the chicken breast into small, uniform cubes and season lightly with sea salt.
Heat the extra virgin olive oil in a large skillet over medium heat, then add the pancetta and chicken.
Sauté the meat for 5-7 minutes until the pancetta is crisp and the chicken is fully cooked and golden brown.
In a small mixing bowl, whisk together the whole egg, egg yolk, Pecorino Romano, and black pepper until the mixture is smooth and pale yellow.
Reserve approximately 0.25 cup of the starchy pasta cooking water, then drain the spaghetti thoroughly.
Turn off the heat under the skillet and add the hot pasta directly to the chicken and pancetta, tossing to coat in the rendered fat.
Slowly pour the egg and cheese mixture over the pasta while stirring rapidly and constantly to create a creamy emulsion.
Add the reserved pasta water one tablespoon at a time as needed to reach a silky, glossy consistency without scrambling the eggs.