Brine the chicken: Combine 1 can of beer, the salt, granulated sugar, hot sauce and bay leaves in a very large bowl and whisk until the salt and sugar dissolve. Add the remaining 2 cans of beer, 4 cups water and the chicken. Cover and refrigerate overnight.
Make the barbecue sauce: Combine the orange juice, vinegar, onion, garlic, ketchup, brown sugar, honey, Worcestershire sauce and chili powder in a small saucepan. Bring to a boil, then reduce the heat to medium low and simmer, stirring occasionally, until slightly thickened, about 20 minutes. Let cool slightly, then puree in a blender until smooth. (The sauce can be made up to 1 day ahead; cover and refrigerate.)
Preheat a grill to medium low and brush the grates with vegetable oil. Remove the chicken from the brine and pat dry with paper towels. Lightly season the chicken with salt, then arrange on the grill, skin-side up. Cover and cook until marked, about 12 minutes per side. Continue cooking, flipping and basting the chicken with the barbecue sauce every 3 to 4 minutes (keep covered in between), until a thermometer inserted into the center of a breast registers 165 degrees F, about 15 more minutes. Transfer to a platter and let rest 5 minutes before serving.