Preheat the oven to 375 degrees F.
Heat the oil in heavy, medium 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 and bring to boil. Continue boiling until the chiles are soft, about 5 minutes. Transfer the mixture to blender and puree. Season with salt and pepper.
Preheat a grill or large grill pan over medium-high heat.
Meanwhile, rub the adobo mixture all over the chicken, using about half of the adobo. 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 chicken breast-side up, place in a baking pan and transfer to the oven. Cook the chicken, basting with the extra adobo sauce every 20 minutes, until a meat thermometer registers an inner temperature of 165 degrees F, about 40 minutes. Serve with corn tortillas to prepare tacos and lime wedges.
When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.