In a resealable plastic bag, combine the beer, butter, garlic, chili powder, brown sugar and salt. Add the drumsticks, seal the bag and let marinate while you proceed.
Preheat a grill or grill pan to high. Microwave the potatoes on high until slightly softened, about 5 minutes. Slice the potatoes lengthwise about 1/4-inch thick. Drizzle both sides generously with olive oil.
Transfer the chicken and potatoes to the grill. Grill the drumsticks, brushing with the beer marinade and turning occasionally, until the skin is golden and crisp and the juices run clear, 20 to 25 minutes Meanwhile, grill the potatoes until grill marks appear, about 3 minutes on each side. Transfer to a plate and sprinkle with salt. Serve the chicken and potatoes with the lime wedges.