Heat the oil in medium heavy saucepan over medium heat. Add the onions and cook until translucent, about 5 minutes. Add the garlic and cook for 3 minutes longer. Add the chiles and cook until darkened on both sides, about 1 minute. Add the broth, bring to a boil and boil until the chiles are soft, about 5 minutes. Transfer the mixture to a blender, add the vinegar and 1 tablespoon water, let cool slightly and puree. Season with salt and pepper.
Preheat a grill or large grill pan over medium-high heat.
Meanwhile, rub about half of the adobo mixture all over the chicken. Sear the chicken breast-side down until grill marks appear, about 6 minutes. Brush some adobo sauce on the other side of the chicken. Turn the grill down to medium and set one side of the grill to indirect heat (see Cook's Note for instructions for the grill pan). Turn the chicken breast-side up, place over the indirect heat side of the grill and cover. Cook the chicken, basting with the extra adobo sauce every 20 minutes, until a meat thermometer registers an inner temperature of 165 degrees F, 30 to 40 minutes.
Serve with corn tortillas, lime wedges, avocado and cilantro.
If using a grill pan, after the initial grilling, turn the chicken breast-side up and transfer to a baking pan. Put in the oven at 375 degrees F and cook the chicken, basting with the extra adobo sauce every 20 minutes, until a meat thermometer registers an inner temperature of 165 degrees F, 30 to 40 minutes.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.