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 large skillet over medium-high heat and sear the chicken for 5-6 minutes per side until golden and cooked through.
Remove the chicken from the skillet, let it rest for 2 minutes, then slice into thin strips.
In the same skillet, reduce the heat to low and sauté the minced garlic for 30 seconds until fragrant.
In a small bowl, whisk together the Greek yogurt, grated parmesan, and the remaining salt and pepper.
Drain the pasta, reserving 2 tablespoons of the starchy cooking water.
Add the pasta, reserved water, yogurt mixture, and baby spinach to the skillet, tossing gently until the sauce is creamy and the spinach is wilted.
Top the pasta with the sliced chicken and serve immediately.