Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and season with salt and black pepper. Cook for 5-6 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the orzo pasta to the skillet and stir to coat it with the oil and onion mixture.
Pour in the chicken broth and milk, then add the dried oregano and thyme. Stir to combine.
Bring the mixture to a boil, then reduce the heat to medium-low and simmer uncovered for 10-12 minutes, stirring occasionally, until the orzo is tender and most of the liquid is absorbed.
Return the cooked chicken to the skillet and stir in the grated Parmesan cheese and chopped spinach.
Cook for an additional 2-3 minutes until the spinach is wilted and the sauce is creamy.
Taste and adjust seasoning with salt and black pepper as needed.
Serve hot, garnished with extra Parmesan if desired.