If you can find a whole chicken cut up in your store, use that. I cannot ever find one that is already cut up. So I will buy a whole chicken and quarter it on the bone, disposing of the spine.
Add chicken to a large pot, cover the chicken with water, and place over med/high heat.
Cook for 30-40 minutes or until the internal temperature reaches 165 F.
Remove from the liquid and place onto a plate to cool to room temperature. 30 minutes.
(OPTIONAL STEP): Reduce the remaining liquid to 1 cup and use instead of chicken stock.
Cut room temperature chicken into 1/2 inch chunks. Cut the onion into a small dice.
In large skillet over med to med/high heat add 1 Tablespoon of oil and Saute the onion for 2-3 minutes, stir often. (some browning is ok). Add the garlic and cook for 1 minute.
Add the cut chicken to the skillet and cook for 1-2 minutes. Add the Chili, cumin and oregano to the chicken and stir well.
Reduce to med heat and add 1/2 of the stock, stirring constantly the liquid will adsorb into the chicken and break it up to shredded consistency. When the chicken is starting to look dry and has adsorbed the liquid. Add the remaining stock and continue stirring until almost dry.
Remove from the heat add the Cilantro and season with salt and pepper as desired.
Place chicken into a large bowl and cover. Refrigerate for 1-2 hours until cool.
Add the cheese and mix until well incorporated.
Fill tortillas for enchiladas, or refrigerate 5 days or freeze 2 months.