Remove the tough outer layers from lemongrass and chop finely. Place it in a food processor along with garlic and shallots. Process to a smooth paste.
Add oil, fish sauce, chili paste, brown sugar and soy sauce. Process to a smooth paste. Transfer to a large bowl.
Add chicken. Coat the chicken in the marinade. Cover and marinate in the refrigerator for at least 30 minutes to 1 hour.Preheat grill to low heat.
Brush the grates with oil. Remove the thighs from the marinade, shaking off any excess. Place them on the grill smooth side up. Cook, covered, for 12-15 minutes. Baste with the marinade. Flip over and cook, covered, for another 12-15 minutes or until no pink remains.
Transfer chicken to a platter and let it rest for 5-10 minutes before serving.