Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente, reserving 1/4 cup of pasta water before draining.
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 until golden brown and cooked through, about 5-6 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 the heat to low and sauté the minced garlic for 30 seconds until fragrant.
In a small bowl, whisk together the Greek yogurt, grated parmesan, lemon juice, and the remaining salt and pepper.
Add the cooked pasta and the yogurt mixture to the skillet, tossing gently to coat.
Gradually add the reserved pasta water one tablespoon at a time until the sauce reaches a smooth, creamy consistency.
Fold the sliced chicken back into the pasta and garnish with freshly chopped parsley before serving.