Heat the olive oil in a large pot over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, carrots, and celery to the pot. Cook for 4 minutes until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute until fragrant.
Pour in the chicken broth and bring the mixture to a boil.
Add the orzo, lemon zest, lemon juice, and dried thyme. Reduce heat to a simmer and cook for 10 minutes, stirring occasionally.
Season with salt and pepper to taste. Remove from heat and stir in the fresh parsley before serving.