Bring a large pot of salted water to a boil and cook the gluten-free 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. Add the chicken and sear for 5-6 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.
Whisk together the Greek yogurt, lemon juice, parmesan cheese, and the remaining salt and pepper in a small bowl.
Reserve 2 tablespoons of the pasta cooking water, then drain the pasta.
Add the cooked pasta and the yogurt mixture to the skillet, tossing gently and adding the reserved pasta water as needed to reach a creamy consistency.
Fold the sliced chicken back into the pasta and garnish with fresh parsley before serving.