Heat olive oil in a large Dutch oven over medium heat. Add diced onions and carrots, sautéing until softened, about 5 minutes. Add minced garlic and cumin, cooking for 1 more minute.

Pour in the chicken broth, chopped Hatch chiles, and chicken breasts. Bring to a gentle boil, then reduce heat to low, cover, and simmer for 20 minutes until the poultry is fully cooked.

Remove the meat to a cutting board and shred it using two forks.

Return the shredded meat to the pot. Stir in the uncooked white rice and fresh corn. Simmer covered for another 20 minutes, or until the rice is tender.

Stir in the chopped cilantro, season with salt and pepper to taste, and serve hot.