Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces to the skillet and season with salt and black pepper. Cook for 5-6 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook for 2-3 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, onion, and garlic mixture.
Pour in the chicken broth, then add dried thyme and dried oregano. Stir well to combine.
Bring the mixture to a boil, then reduce heat to medium-low and cover the skillet.
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 the cheeses are melted and the mixture is creamy.
Taste and adjust seasoning with additional salt and black pepper if needed.
Remove from heat and sprinkle chopped fresh parsley on top before serving.