Cook the Onion:
Heat the olive oil in a large pot over medium heat. Once warmed, add the diced onion and oregano. Sauté, stirring frequently, for 3 to 4 minutes, until the onion softens and becomes translucent. Season with salt and black pepper.
Simmer the Soup:
Introduce the fire-roasted diced tomatoes, chicken broth, corn kernels, and uncooked rice into the pot. Bring the mixture to a boil over high heat. Lower the heat to a gentle simmer and allow it to cook for 18 to 20 minutes, or until the rice achieves a tender texture.
Incorporate the Chicken:
Stir in the shredded chicken and let the soup continue simmering for 1 to 2 minutes, or until the chicken is thoroughly heated. Taste and adjust the seasoning with additional salt and pepper, if needed.
Serve the Soup:
Portion the soup into individual bowls. Garnish with fresh cilantro leaves and lime wedges. Serve immediately with warm corn or flour tortillas on the side.