In a mixing bowl, whisk together olive oil, minced garlic, lemon juice, lemon zest, oregano, salt, and pepper.
Place the chicken breasts in the bowl and coat them thoroughly with the marinade. Let them marinate for at least 10 minutes.
While the chicken marinates, rinse the rice under cold water until the water runs clear to remove excess starch.
In a pot, bring 2 cups of chicken broth (or water) to a boil. Add the rinsed rice and a pinch of salt, then reduce the heat to low. Cover and simmer for about 18-20 minutes, or until the rice is tender and liquid is absorbed. Fluff with a fork.
In a skillet over medium heat, add a little olive oil if needed. Cook the marinated chicken breasts for about 6-7 minutes on each side, or until they are cooked through and have a golden brown color (internal temperature should reach 75°C or 165°F).
Once the chicken is cooked, let it rest on a cutting board for a few minutes before slicing.
Serve the sliced chicken over the fluffy rice and drizzle any remaining juices from the skillet over the top. Garnish with chopped fresh parsley if desired.