Bring a large pot of salted water to the boil. Cook your pasta according to package directions minus one minute.
Heat the olive oil and guanciale in a large skillet over medium heat for 2-3 minutes until the fat renders.
Add the garlic and capers. Cook, stirring occasionally, for 1-2 minutes.
Add the chicken and wine. Bring the heat up to medium high and cook until the wine is reduced by half, 2-3 minutes, flipping the chicken to ensure even cooking.
Add the cream. Reduce the cream by half, stirring occassionally to form an emulsified, glossy sauce, 2-3 minutes.
Reduce heat to low or remove from heat, then add cheese and black pepper. Whisk until cheese is melted, 1 minute. Taste and add salt as needed.
Reserve 1/2 cup pasta water, then drain the pasta and add to the pan. Turn the heat up to medium high and gently toss pasta for 1 minute or until every strand or piece of pasta is properly coated. Add pasta water, 1 tablespoon at a time, if needed.
Serve immediately, with extra grated cheese on top