1. At least 1 hour before grilling, soak wood chips in enough water to cover.
2. Meanwhile, remove the neck and giblets from chicken, if necessary. Place chicken in a large plastic bag set in a deep bowl. Pour beer into the chicken cavity and over the chicken; seal bag. Marinate in the refrigerator for 1 hour, turning bag occasionally.
3. Drain chicken, discarding marinade. Sprinkle chicken body cavity with garlic salt and black pepper. Cut limes in half. Squeeze juice from 2 of the lime halves. In a small bowl combine lime juice and the ground red chile peppers; set aside. Squeeze juice from remaining lime halves into chicken body cavity; place squeezed lime halves inside chicken cavity. Skewer the neck skin to the back. Twist wing tips under back. Tie legs to tail with 100%-cotton string.
4. Brush a thin, even coat of the chile pepper mixture evenly over skin of chicken; cover and chill for 20 minutes.
5. Drain wood chips. Place them in the center of a 12-inch square of foil. Bring up the 2 opposite edges of foil and seal with a double fold. Fold ends to completely enclose the chips. Use a knife to carefully make several small slits in the top of the foil packet.
6. Arrange medium-hot coals around a drip pan. Pour 1 inch of water into the drip pan. Place packet of wood chips on the grill rack over coals or directly on coals. Cover and heat about 10 minutes or until chips begin to smoke. Test for medium heat above the pan. Place chicken, breast side up, on grill rack over drip pan. Cover and grill for 1-1/4 to 1-1/2 hours or until an instant-read thermometer inserted in an inside thigh muscle registers 180 degrees F, chicken is no longer pink, and drumsticks move easily in their sockets.
7. Remove chicken from grill. Cover with foil; let stand for 10 minutes before carving. Remove and discard lime halves. If desired, garnish each serving with thin slices of lime.