In a large pot, heat the olive oil over medium heat. Once hot, add the diced onion and sauté for about 5 minutes until the onion is translucent. Add the minced garlic and cook for an additional minute, stirring frequently to prevent burning.
Stir in the ground cumin, dried oregano, and chili powder. Cook for about 30 seconds until the spices become fragrant, releasing their essential oils.
Carefully add the low-sodium chicken broth to the pot, scraping any bits stuck to the bottom to incorporate all the flavors.
Bring the broth to a gentle boil, then add the long-grain white rice and shredded chicken. Stir well to combine and reduce the heat to a simmer.
After the rice has been simmering for about 15 minutes, add the diced tomato. Continue to simmer until the rice is cooked through and tender, about 5-10 more minutes.
Taste the soup and season with salt and pepper to your liking. Once satisfied, remove from heat and ladle the soup into bowls. Garnish with freshly chopped cilantro and serve with lime wedges on the side.