Heat the olive oil in a large pot or deep skillet over medium-high heat.
Add the chicken pieces and cook, stirring occasionally, until browned and cooked through, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion and cook until softened, about 3 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the diced zucchini and cook for 2-3 minutes until slightly tender.
Stir in the orzo pasta, dried oregano, and dried thyme. Cook for 1 minute, stirring to coat the orzo with the oil and vegetables.
Pour in the chicken broth and season with salt and freshly ground black pepper to taste.
Bring the mixture to a boil, then reduce heat to medium-low and simmer, uncovered, stirring occasionally, until the orzo is tender and most of the liquid is absorbed, about 10-12 minutes.
Return the cooked chicken to the pot and stir to combine. Cook for an additional 2 minutes to heat through.
Remove from heat and stir in the grated Parmesan cheese and chopped fresh parsley.
Serve immediately.