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 on all sides but not fully cooked through. Remove chicken 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 diced zucchini and cook for 2-3 minutes until slightly tender.
Stir in the rinsed rice and cook for 1-2 minutes to lightly toast the rice.
Pour in the chicken broth, then add the dried oregano, salt, black pepper, and crushed red pepper flakes. Stir to combine.
Return the browned chicken pieces to the skillet, nestling them into the rice mixture.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 18-20 minutes until the rice is cooked and the liquid is absorbed.
Remove from heat and let it sit, covered, for 5 minutes.
Fluff the rice with a fork, stir in the chopped fresh parsley, and serve warm.