Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and season with salt and 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 1 minute until fragrant.
Add the orzo pasta to the skillet and stir to coat with the oil and onion mixture.
Pour in the chicken broth, then add dried thyme, dried oregano, crushed red pepper flakes, and a pinch of salt and pepper. Stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low. Cover and 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 to combine.
Add the softened Boursin cheese and grated Parmesan cheese to the skillet. Stir until the cheeses are fully melted and the mixture is creamy.
Taste and adjust seasoning with additional salt and pepper if needed.
Remove from heat and sprinkle with chopped fresh parsley before serving.