Bring a pot of water to a boil and cook the spaghetti until al dente, reserving 0.25 cup of the starchy pasta water before draining.
In a large skillet over medium heat, sauté the diced pancetta until it becomes golden and crispy, then remove and set aside on a paper towel.
In the same skillet using the rendered fat, add the diced chicken breast and minced garlic, cooking until the chicken is browned and cooked through.
While the chicken cooks, whisk together the whole egg, egg whites, and grated parmesan cheese in a small bowl until well combined.
Remove the skillet from the heat, add the cooked pasta to the chicken, and quickly pour in the egg mixture while stirring constantly.
Gradually add the reserved pasta water a tablespoon at a time until the sauce is creamy and coats the noodles, then stir in the crispy pancetta.
Season with sea salt and plenty of freshly cracked black pepper before serving immediately.