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 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 and whole milk, then add the salt, black pepper, and crushed red pepper flakes. Stir to combine.
Bring the mixture to a boil, then reduce 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 lemon zest, lemon juice, butter, and grated Parmesan cheese.
Cook for an additional 2-3 minutes, stirring frequently, until the sauce is creamy and heated through.
Remove from heat and stir in the chopped fresh parsley.
Serve immediately.