Place the sauce ingredients into a Dutch oven. Place the chicken breasts into the sauce.
Preheat the oven to 300 degrees F. Place the cover on the Dutch oven and cook in the oven for 2 hours.
Remove the pot from the oven and place the chicken, one breast at a time on a plate. Use two forks to pull the chicken and shred it. Place the shredded chicken back into the Dutch oven.
Place the Dutch oven back into the oven and lower the temperature to 250 degrees F. Cook for another 2 hours to marry the flavors.
To thicken the sauce, put the entire pot on the stovetop and cook over medium heat. Add 2 tablespoons of cornstarch and stir with a wooden spoon as it simmers. The sauce will thicken in about 5 minutes.
Cook Chicken in Slow Cooker
Place the sauce ingredients into a slow cooker. Place the chicken breasts into the sauce.
Cook on low for 4 hours.
Shred the chicken and continue to cook on low for another 2 hours for the flavors to marry.
Notes
NOTE: Find canned Chipotle peppers in Adobo sauce in the Hispanic foods aisle.They will break up as the cook. Should you want a little less pop of spice, remove any that are still whole after the cooking process.