In a blender or food processor, combine the lemongrass, garlic, fish sauce, light soy sauce, dark soy sauce, brown sugar, and neutral oil. Blend until the lemongrass and garlic form a smooth paste.
Place the chicken thighs in a bowl or resealable bag. Pour the marinade over the chicken, making sure each piece is well coated. Cover (or seal) and refrigerate for at least 3 hours, ideally overnight — longer marinating yields deeper flavor.
When ready to cook, preheat a grill, heavy-bottomed skillet, or grill pan over medium-high heat. Lightly oil the surface.
Remove chicken from the marinade (let any excess drip off). Place on hot grill/pan. Cook about 5–6 minutes per side (depending on thickness), until chicken is cooked through and edges are nicely caramelized and slightly charred. Watch carefully to avoid burning.
Transfer chicken to a plate and let it rest for a few minutes to allow juices to settle.
Garnish with lime wedges, sliced fresh chili and fresh coriander/cilantro. Serve hot with jasmine or coconut rice, and fresh cucumber or salad if available.