Prepare chicken and sauce: Place chicken in a dutch oven. Add 2 cups of gf chicken broth. Then add just enough water to cover. Bring to a low boil over a high heat, then reduce the heat so that the poaching liquid barely bubbles. Cover and cook until the meat releases clear juices when pierced with a fork, about 12 minutes. Remove the meat from the stock and let it stand until it is cool enough to handle. Then shred the meat into bite-sized pieces.
Meanwhile, heat 1 tablespoon of olive oil in a medium saucepan over medium heat and sauté onion seasoned with chili powder, cumin and salt for 5 minutes. Add the garlic, tomatoes, vinegar, and cilantro, stir, cover and simmer for 15 more minutes. Then toss shredded chicken with 1 1/2 cups of the sauce in a mixing bowl.
Assemble: Spoon a generous amount of sauce in the bottom of a 9 x 13 baking dish.
Heat 1 tablespoon of oil in a skillet. One at a time, cook the corn tortillas on low to soften them, about 30 seconds on each side. Lay the first hot tortilla in the baking dish. Spoon shredded chicken and sauce mixture down the center. Top with cheese and tightly roll. Repeat for the remaining tortillas. Finally, top with remainder of sauce and shredded cheese.