Heat a deep stock pot over high heat until boiling.
While the water is boiling for the pasta, heat 1 tbsp. olive oil over medium-high heat in a large skillet. Season the chicken with salt and pepper.
Place the seasoned chicken into the hot oil and cook until well-browned and cooked through, about 4-6 minutes per side. Remove from heat and chop or shred into bite-size pieces, reserving the oil from the pan. Set the chicken aside.
Reserve a cup of pasta cooking water before draining.
In a large mixing bowl, add the cooked and drained pasta, followed by the goat cheese, greek yogurt, garlic, and rosemary. Add in the reserved pasta water to loosen up the sauce.
Stir together until the cheese has melted and the sauce is creamy.
Add the chicken, and stir to combine.