Heat olive oil in a large pot over medium-high heat. Season the chicken pieces with salt and pepper, then add them to the pot. Cook until the chicken is browned and cooked through, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion and garlic. Sauté until the onion is soft and translucent, about 3-4 minutes.
Add the orzo to the pot and cook for 1-2 minutes, stirring frequently to toast the pasta.
Pour in the chicken broth and water. Bring to a boil, then reduce heat and let it simmer for about 10 minutes, or until the orzo is tender and most of the liquid is absorbed.
Stir in the lemon zest, lemon juice, heavy cream, and Parmesan cheese. Cook for another 2-3 minutes until the sauce is creamy and well combined.
Add the cooked chicken back to the pot along with the fresh spinach. Stir until the spinach is wilted and everything is heated through.
Garnish with chopped parsley before serving.