In a mini food processor, process the cilantro, fish sauce and pepper to a coarse puree. Coat the chicken with the marinade. Let stand at room temperature for 20 minutes.
In a bowl, combine the dissolved tamarind with the fish sauce, lime, garlic, chile, sugar and water.
Preheat the oven to 400°. Light a grill. Rub the chicken with the oil and rub the grill with an oiled paper towel. Grill the chicken over moderately high heat, turning, until charred, 12 minutes. Transfer the chicken to a baking sheet and roast for 30 minutes, until cooked.
Just before serving, stir the cilantro into the dipping sauce and serve with the chicken.
Tamarind concentrate is available at Indian and Latin food shops.
Nutrition data per one serving.