Combine vinegar, jalapeño juice, sugar, salt, water and chicken thighs in plastic food-storage bag. Seal; turn over to coat. Refrigerate 30 minutes to marinate.
Meanwhile, in medium-size saucepan, heat oil over medium heat. Add onion and garlic; cook until softened, about 7 minutes. Stir in beer; bring to a simmer. Add ketchup, brown sugar, molasses, pickled jalapeños and juice, mustard, Worcestershire, lemon juice and salt; simmer over medium heat, uncovered, until a thick sauce, 30 to 35 minutes.
Meanwhile, prepare outdoor grill with medium-hot coals, or heat gas grill to medium-high, or see Broiler Method, below.
Remove chicken from marinade. Place on grill. Cover grill; cook until browned, about 13 minutes. Flip chicken over. Cook chicken until internal temperature registers 180 degrees F on instant-read thermometer, about 15 minutes. Remove from heat. Let stand until cool enough to handle.
Remove meat from bones and shred. Stir together with cooked sauce in saucepan. Gently heat through.
Make 16 sandwiches, about 1/4 cup shredded chicken for each, and top filling with pickles, if desired. Serve warm. Makes 8 servings.
Heat broiler. Coat broiler-pan rack with cooking spray. Place the chicken thighs on rack. Broil 4 inches from the heat following directions in step 4.