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 non-stick skillet over medium-high heat and sear the chicken for 5-6 minutes per side until fully cooked through.
Remove the chicken from the pan, let it rest for a few 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, parmesan cheese, and chicken broth in a small bowl until smooth.
Add the yogurt mixture to the skillet over very low heat, stirring constantly to prevent curdling until the sauce is warm.
Drain the pasta, reserving a tablespoon of pasta water, and add the noodles to the skillet.
Toss the pasta and sliced chicken in the sauce, adding the reserved pasta water if needed to reach a creamy consistency.
Garnish with fresh parsley and the remaining salt and pepper before serving.