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 5-7 minutes per side until golden and 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 medium and add the minced garlic, sautéing for 1 minute until fragrant.
Whisk in the chicken broth, scraping up any browned bits from the bottom of the pan.
Lower the heat to low and stir in the Greek yogurt and parmesan cheese until smooth, being careful not to let the yogurt boil.
Add the baby spinach to the sauce and stir until just wilted.
Toss the cooked fettuccine and sliced chicken into the sauce until well coated, adding a splash of pasta water if needed to reach your desired consistency.
Season with the remaining salt and pepper before serving.