Cook the Onion
Warm the olive oil in a large pot over medium heat. Add the diced onion and oregano, sautéing for 3 to 4 minutes until the onion becomes soft and translucent. Season with salt and black pepper.
Simmer the Soup
Stir in the fire-roasted diced tomatoes, chicken broth, corn, and uncooked rice. Raise the heat to bring the mixture to a boil, then reduce to a gentle simmer. Cook for 18 to 20 minutes, or until the rice is tender.
Incorporate the Chicken
Add the shredded chicken to the pot and continue simmering for 1 to 2 minutes, just until the chicken is fully heated. Taste and adjust seasoning as necessary.
Serve the Soup
Ladle the soup into individual bowls, garnishing with fresh cilantro and lime wedges. Serve immediately alongside warm corn or flour tortillas.