Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove 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 1 minute until fragrant.
Add the orzo pasta to the skillet and stir to coat with the oil, onion, and garlic mixture.
Pour in the chicken broth, then add the dried thyme, dried oregano, salt, and black pepper. Stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low and cover. Simmer 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 Boursin cheese and grated Parmesan cheese until melted and creamy.
Add the chopped spinach and cook for an additional 2 minutes until wilted and incorporated.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve warm, garnished with extra Parmesan cheese if desired.