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 on both sides with sea salt and black pepper.
Heat olive oil in a non-stick skillet over medium-high heat and sear the chicken for 5-6 minutes per side until cooked through, then remove and slice into strips.
In the same skillet, reduce heat to medium and add the minced garlic, sautéing for 1 minute until fragrant.
Whisk together the Greek yogurt, chicken broth, and grated parmesan cheese in a small bowl until smooth.
Pour the yogurt mixture into the skillet with the garlic, stirring constantly on low heat for 2 minutes to thicken without boiling.
Drain the fettuccine, reserving a splash of pasta water, and toss the noodles into the skillet with the sauce.
Add the sliced chicken back to the pan and toss everything together, adding a tablespoon of pasta water if needed to reach a creamy consistency.
Garnish with fresh chopped parsley and serve immediately.