Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente.
While the pasta cooks, season the chicken breast with half of the sea salt and black pepper.
Heat the olive oil in a skillet over medium-high heat and sear the chicken for 5-6 minutes per side until fully cooked, then set aside to rest before slicing.
In the same skillet, reduce heat to low and add the minced garlic, sautéing for 1 minute until fragrant.
In a small bowl, whisk together the Greek yogurt, grated parmesan, and the remaining salt and pepper.
Reserve 2 tablespoons of the starchy pasta water, then drain the noodles.
Add the cooked noodles, yogurt mixture, and reserved pasta water to the skillet, tossing gently over low heat until the sauce is creamy and coats the pasta.
Top the fettuccine with the sliced chicken and garnish with fresh chopped parsley before serving.