Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente.
Season the chicken breast with sea salt and black pepper on both sides.
Heat olive oil in a large 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 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 in the Greek yogurt, chicken broth, and grated parmesan cheese until the sauce is smooth and creamy.
Add the cooked pasta and sliced chicken back into the skillet, tossing gently to coat everything in the velvety sauce.
Garnish with fresh chopped parsley before serving.