Bring a large pot of salted water to a boil and cook the brown rice fettuccine according to package directions until al dente.
Before draining the pasta, reserve approximately 0.25 cup of the starchy pasta water and set it aside.
While the pasta cooks, slice the chicken breast into thin strips and season evenly with the sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken strips and sear for 5-6 minutes until golden brown and cooked through.
Reduce the heat to low and add the minced garlic to the skillet, sautéing for 30 seconds until fragrant.
In a small bowl, whisk together the Greek yogurt and grated parmesan cheese until smooth.
Add the cooked pasta and the yogurt mixture to the skillet with the chicken, slowly adding the reserved pasta water one tablespoon at a time to reach a creamy consistency.
Toss everything together gently over low heat just until the sauce is warmed through, being careful not to boil the yogurt.
Garnish with freshly chopped parsley and serve immediately.