Heat the olive oil in a large pot over medium heat. Add the chicken pieces, salt, and pepper. Cook for 5 to 6 minutes until the chicken is lightly browned on all sides.
Stir in the minced garlic and dried oregano. Cook for 1 minute until the garlic becomes fragrant.
Add the rice to the pot and stir to coat it with the oil and seasonings. Pour in the chicken broth along with the lemon zest and lemon juice.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot and simmer for 18 minutes without lifting the lid.
Remove the pot from the heat and let it sit covered for 5 minutes. Fluff the rice with a fork, then stir in the chopped parsley.
Serve the dish warm with lemon wedges on the side.