Place the chicken, onion, and garlic in a large pot. Fill it with water until the chicken is submerged.
Bring to a boil. Skim off all of the scum that floats to the top. Add in the celery and parsley. Simmer for 45 minutes over medium heat until the chicken is completely cooked through. Drain the chicken, saving a cup of the stock you just created. Set aside.
Dry toast the pasilla peppers in a skillet for 5 minutes on all sides. Place in a bowl of hot water for 15 minutes. Remove the seeds and drain the water.
Dry toast the tomato, onion, and garlic for 5 minutes until charred on all sides.
Place the pasilla peppers, tomatoes, onion, garlic, and the chicken stock in a blender.
Purée until smooth.
Heat up the cooking oil in a large saucepan over medium heat. Pour the sauce through a fine strainer to remove the seeds into the saucepan. Simmer for 5 minutes.
Add in the Mexican chocolate tab, salt, and pepper. Simmer until the tablet has completely dissolved.
Place the chicken pieces back into the mole sauce. Simmer for 15 minutes over medium heat; continuously basting the chicken with the sauce.