Prep the chiles:

1. Combine the vinegar, water, sugar, and salt in a small pot and bring to a simmer. Add the garlic and chiles and simmer for at least 5 minutes.
2. Remove from the heat and weight-down the chiles to keep them submerged while they cool for at least 3 hours.
3. Check each hour; if the chiles do not seem to be rehydrating, bring the pot back to a simmer for a few minutes then begin cooling again.
4. Tear open the chiles and discard the seeds and stem base, then chop what remains. Add to the 3 tbsp pickling brine.

Cook the tinga:

1. Add the tomatoes and their juice and the diced pickled moritas and the reserved brine to a blender. Blend just until the pepper bits are broken down small enough.
2. Set a large skillet over medium-high heat. Coat the bottom liberally with olive oil.
3. Add the onion and stir until it begins to brown. Add the garlic and cook for an additional minute, stirring often. Transfer to a bowl — try to leave as much oil behind as you can.
4. Brown the chicken in batches without crowding the skillet. Season the uncooked side of the chicken with a small amount of salt and pepper right before turning each batch for the first time. Transfer each batch to the bowl holding the cooked onion and garlic.
5. Add the chicken, onion, and garlic back to the skillet. Pour the blended tomato and chile mixture over the chicken and sprinkle-on the oregano. Stir then bring to a gentle simmer for 10 to 15 minutes.
6. Taste the sauce and add salt or more morita brine to taste.

Serve the tinga with a generous amount of sauce in small flour street taco tortillas with grated sharp cheddar and dice avocado or guacamole.