From http://patismexicantable.com/2010/07/chicken-tinga.html

Ingredients

• 3 tablespoons of sunflower or corn oil
• 1/2 white onion, finely chopped
• 2 garlic cloves, chopped
• 8 roma tomatoes, rinsed
• 2 tomatillos, husks removed, rinsed
• 1/2 teaspoon crumbled, dried oregano
• 1/4 teaspoon dried marjoram
• 1/4 teaspoon dried thyme
• 1 1/2 to 2 teaspoons salt
• 1/4 teaspoon black pepper, freshly ground
• 2 tablespoons sauce from Chipotle Chiles in Adobo, can add more chiles for heat
• 5 cups shredded, cooked chicken

Method

1. Place the rinsed tomatoes and tomatillos in a medium saucepan and cover them with water over a medium heat.
2. Simmer for 8 to 10 minutes, or until the tomatoes and tomatillos are soft, thoroughly cooked and smooshy but not coming apart.
3. Remove the tomatoes and tomatillos with a slotted spoon and place in a blender or food processor and process until smooth
4. Heat the oil in a large and deep pan over a medium heat. Once it is hot but not smoking, stir in the onion and cook until soft and translucent for about 5 to 6 minutes
5. Stir in the garlic and cook until it becomes fragrant and lightly browned, about 1 minute
6. Pour the tomatillo/tomato sauce on top and sprinkle the oregano, marjoram, thyme, salt and black pepper. Spoon the chipotle Chiles in Adobo sauce as well.
7. Let the sauce simmer, stirring now and then, until it seasons and deepens its red colour, for about 10 to 12 minutes. You may want to partially cover the pan as the sauce may want to jump out over your burners
8. Toss in the chicken and combine with the sauce. Let it cook, stirring casually as it does, until the chicken has absorbed almost all of the juices and the mix is moist but not juicy

Use a couple of cups as filling for quesadillas with some grated cheese.