Bring a pot of salted water to a boil and cook the whole wheat fettuccine according to package directions until al dente.
Reserve 0.25 cup of the pasta cooking water, then drain the noodles and set them aside.
Season the chicken breast with half of the sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and cook the chicken until golden brown and cooked through, about 5-7 minutes per side.
Remove the chicken from the pan, let it rest for a few minutes, then slice it into thin strips.
In the same skillet, reduce heat to low and sauté the minced garlic for 1 minute until fragrant.
Whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water in a small bowl until smooth.
Add the pasta and the yogurt mixture to the skillet, tossing gently over low heat until the sauce coats the noodles.
Stir in the sliced chicken and remaining salt and pepper, then garnish with fresh parsley before serving.