In a food processor, whirl coconut, chilies, and 2 tablespoons hot water until finely ground.
Add spice paste, salt, pepper, and chicken; whirl until well mixed.
Trim root ends from lemon grass. Trim tops to make stalks 6 to 8 inches long. Remove coarse outer leaves.
Dipping hands in cool water often to reduce sticking, mound about 1/4 cup chicken mixture around thick end of each lemon grass stalk (or 2 tablespoons on one end of each soaked wood skewer). Gently squeeze chicken mixture around each stalk (or skewer) into a 4-inch log. Place chicken sticks in a single layer in a flat pan.
Lay chicken satay on a lightly oiled grill over hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Cook, turning as needed to brown evenly, 5 to 6 minutes. Serve hot or at room temperature.