In a large Dutch oven or heavy pot, heat oil over medium-high. Season chicken on both sides with salt and pepper. Working in batches, brown chicken on both sides, about 6 minutes total; transfer to a plate.
Reduce heat to medium. Add onion and sauté until soft, about 5 minutes. Add a 1/2 cup water to help release browned bits from the bottom of the pot.
Add garlic, cumin, and chiles; cook until garlic is soft and fragrant, 2 minutes. Add tomatoes and 1 teaspoon salt and cook until tomatoes begin to break down and release their juices, 3 minutes. Stir in chicken stock and return chicken and any accumulated juices to pot. Cover, reduce to a simmer, and cook 25 minutes.
Remove several pieces of chicken and stir in rice, making sure it is completely submerged in liquid. Replace chicken, cover, and cook until rice is tender and liquid has been absorbed, 25 to 30 minutes more. Serve with lime wedges and cilantro.
For Burritos: Simply cut chicken into bite-size pieces before cooking. Heat flour tortillas according to package directions. Top with filling, Sour cream and cheddar cheese, tuck the ends in and roll up tightly.