Heat 1 tablespoon olive oil in a large pot over medium heat. Add 1 medium onion (diced) and cook, stirring occasionally, until translucent, about 5 minutes.
Add 2 cloves garlic (minced), 1 teaspoon ground cumin, 1/2 teaspoon dried oregano, and 1/4 teaspoon chili powder. Cook, stirring, about 1 minute, until fragrant.
Pour in 6 cups low-sodium chicken broth and bring to a boil over medium-high heat.
Stir in 1 cup long-grain white rice. Reduce heat to low, cover, and simmer for 20 minutes, stirring once or twice to prevent sticking.
Add 2 cups cooked chicken (shredded) and 1 large tomato (diced). Season with salt and pepper to taste. Continue to simmer until the rice is tender and the chicken is heated through, about 10 minutes.
Taste and adjust seasoning if needed. Serve hot, garnished with chopped fresh cilantro and lime wedges.