Add chicken ingredients to a large skillet with high walls or just a pot. Add enough water to just cover the chicken and bring to a simmer. Simmer, covered, until chicken is cooked, about 20-30 minutes.
Remove chicken and let cool for a few minutes. Strain stock and save for later! Once chicken is cool enough to handle, remove skin and excess fat and shred.
For sauce, combine all ingredients in a blender and pulse until combined.
Add sauce to a large skillet and bring to a simmer. Simmer for a few minutes until it starts to thicken.
Add chicken to sauce and continue to simmer until sauce is really thick and sticking to chicken well.
Serve tacos with a variety of toppings including red onion, radishes, limes, and cilantro.