With tomato paste, fish sauce, garlic, sugar, salt, and pepper in medium bowl until smooth. Add chicken and, using your hands, coat chicken evenly. Cover and refrigerate for at least 1 hour or up to 12 hours.

2A. FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter three-quarters filled with charcoal briquettes (4 ½ quarts). When top coals are partially covered with ash, pour evenly over grill. Set grill grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.

2B. FOR A GAS GRILL: Turn all burners to high; cover; and heat grill until hot, about 15 minutes. Leave all burners on high and turn off other burner(s).

While grill heats, thread chicken onto skewers, rolling or folding pieces as necessary to form 1-inch pieces and alternating leaner pieces with fattier pieces (fold any excess fat onto skewers as needed to keep it from hanging loose).

Clean and oil cooking grate. Place kebabs directly over coals (over primary burner if using gas) and cook (covered if using gas) until well browned and slightly charred, 2 to 2 ½ minutes. Turn one-quarter turn and cook until well browned and slightly charred, 2 to 2 ½ minutes. Repeat, turning kebabs, until all sides are browned and charred and meat registers 175 degrees, about 12 minutes in total, rearranging skewers halfway through cooking to ensure even browning. Transfer kebabs from grill to platter. Let rest for 5 minutes. Serve.