Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and cook for 4-5 minutes, stirring occasionally, until lightly browned but not fully 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 with oil and onion mixture.
Pour in the chicken broth and stir in dried oregano, dried thyme, salt, and black pepper.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered for 8 minutes.
Add the broccoli florets and the partially cooked chicken back into the skillet. Stir to combine.
Cover and cook for an additional 7-8 minutes, or until the orzo is tender, the chicken is cooked through, and the broccoli is bright green and tender-crisp.
Remove the skillet from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve immediately.