Finely mince the tender lower 3 to 4 inches of the lemongrass stalks to make about 3 tablespoons. Mix with garlic, shallot, fish sauce, soy sauce, brown sugar, lime juice, oil and pepper.
Unfold thighs and coat with the marinade. Cover and refrigerate for 30 minutes; the prep time includes this rest.
Heat an outdoor grill to about 400°F with a cooler indirect area and clean the grate. Lift chicken from the marinade and discard the remaining used marinade.
Grill for 6 to 8 minutes per side until browned in patches and the thickest meat reaches at least 165°F, moving pieces to the cooler area if their edges darken too quickly.
Rest for 5 minutes, then slice across the thicker folds and serve.