Fill large pot with 12 cups water. Place pot on stovetop over high heat and bring water to rolling boil.
When water begins to boil, add 1 tablespoon sea salt to pot and stir to incorporate. Allow water to resume boiling.
When water begins to boil again, add 8 ounces uncooked bucatini. Boil pasta according to instructions on pasta packaging, reducing cook time by 1 minute.
When pasta is just al dente, pour water and pasta into colander and drain well. Set pasta aside.
Add 6 ounces pancetta to large skillet, then place skillet on stovetop over medium-low heat. Sauté pancetta, stirring as needed, approximately 6 to 8 minutes or until crisp.
Once crisp, use slotted spoon to transfer pancetta to first bowl and set aside. Do not drain skillet.
Return skillet to stovetop and increase heat to medium-high. Add 8 ounces boneless, skinless chicken breasts to skillet. Sear chicken 1 minute, then stir chicken and sear 1 minute more.
Continue cooking chicken, stirring as needed, until chicken is seared on all sides and reaches 160° Fahrenheit internally.
When chicken is cooked, transfer chicken to second bowl and set aside.
Let skillet cool slightly, then pour in 2 cups half-and-half. Reduce heat on stovetop to low, then return skillet to burner. Simmer half-and-half on low heat until warmed through.
Add 4 large egg yolks (at room temperature) to skillet. Whisk until egg yolks are fully incorporated into half-and-half.
Remove skillet from heat and let cool slightly. Add 1 ½ cups grated fresh parmesan to skillet and whisk to incorporate. Return skillet to heat.
Add 1 teaspoon freshly ground black pepper and whisk to incorporate. Simmer sauce, whisking often, until parmesan is completely melted and sauce is smooth.
Return pancetta and chicken to skillet, then add cooked pasta. Toss ingredients together until well incorporated.
Divide chicken carbonara between serving bowls. Top each serving with additional grated fresh parmesan and serve immediately.