Bring a large pot of salted water to a boil and cook the whole wheat 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 olive oil in a medium skillet over medium-high heat and sear the chicken for 5-7 minutes per side until golden and cooked through.
Remove the chicken from the skillet, let it rest for 3 minutes, then slice into thin strips.
In the same skillet, reduce heat to low and add the minced garlic, sautéing for 30 seconds until fragrant.
Reserve 2 tablespoons of the hot pasta water, then drain the noodles.
In a small bowl, whisk together the Greek yogurt, parmesan cheese, remaining salt, pepper, and the reserved pasta water to create a smooth sauce base.
Add the cooked fettuccine and sliced chicken back into the skillet with the garlic, pour the yogurt mixture over the top, and toss gently on low heat until the sauce coats the noodles evenly.
Garnish with freshly chopped parsley and serve immediately.