Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and cook until browned on all sides, about 5 minutes. Remove the chicken and set aside.
In the same skillet, add the chopped onion and cook until softened, about 3 minutes.
Add the minced garlic and cook for 30 seconds until fragrant.
Stir in the rinsed rice and cook for 1-2 minutes, stirring constantly to lightly toast the rice.
Add the diced zucchini, chicken broth, dried oregano, paprika, salt, black pepper, and crushed red pepper flakes. Stir to combine.
Return the browned chicken pieces to the skillet, spreading them evenly over the rice mixture.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 18-20 minutes, or until the rice is tender and the chicken is cooked through.
Remove from heat and let it sit covered for 5 minutes.
Fluff the rice with a fork and sprinkle with chopped fresh parsley before serving.