Heat olive oil in a large skillet over medium-high heat.
Season the chicken pieces with kosher salt and black pepper.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove chicken from 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 with the oil and onion mixture.
Pour in the chicken broth, heavy cream, lemon juice, lemon zest, dried oregano, and crushed red pepper flakes. Stir to combine.
Bring the mixture to a simmer, then reduce heat to medium-low and cover the skillet.
Cook 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.
Cook for an additional 2 minutes until the chicken is heated through and the sauce is creamy.
Remove from heat and sprinkle with chopped fresh parsley before serving.