Heat olive oil in a pot over medium heat, then add onion, oregano, salt, and pepper. Cook until the onion softens and becomes translucent. This step releases flavor that forms the base of the soup.
Add tomatoes with their juices, chicken broth, corn, and rinsed rice. Bring the mixture to a boil, then reduce heat and simmer about 18–20 minutes. The rice absorbs flavor while cooking until tender.
Stir in shredded cooked chicken and simmer briefly until warmed through. Taste and adjust seasoning if needed. Serve hot, topping each bowl with lime juice and cilantro.