Warm olive oil in a large pot over medium heat. Add onion, carrots, and celery; cook until soft and fragrant, about 5 to 7 minutes. Stir in garlic and cook 30 seconds.
Add rinsed rice, diced chicken, dried oregano or thyme, bay leaf, and chicken broth. Scrape the pot to lift any browned bits.
Bring to a gentle boil, then reduce heat and simmer uncovered 15 to 18 minutes, stirring occasionally, until rice is tender and chicken is cooked through.
Remove bay leaf. Stir in lemon zest and juice. Season with salt and pepper, then fold in parsley just before serving.
Ladle into bowls and add an extra squeeze of lemon if desired.