In a large pot or Dutch oven, heat the olive oil over medium heat. Season the chicken pieces with salt and pepper, then add them to the pot. Cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the diced onion and sauté for about 3-4 minutes until translucent. Add the minced garlic and cook for an additional 1 minute until fragrant.
Stir in the orzo pasta and cook for 1-2 minutes, allowing it to toast slightly.
Pour in the chicken broth, lemon zest, lemon juice, oregano, and red pepper flakes (if using). Bring to a boil, then reduce the heat to a simmer.
Add the cooked chicken back into the pot and let everything simmer for about 10-12 minutes, or until the orzo is tender and has absorbed most of the liquid. Stir in the chopped spinach until wilted.
Taste and adjust seasoning with more salt and pepper if needed. Serve hot, garnished with fresh parsley and grated Parmesan cheese.