Grind together lemon grass, garlic, ginger, small onions, green chillies, salt, turmeric powder, lemon juice, fish sauce, tamarind pulp and ½ cup coconut milk to a fine paste.
Transfer into a bowl, add chicken pieces. Rinse the mixer jar with ½ cup coconut milk and pour over the chicken. Let it marinate for at least 12 hours in a refrigerator.
Heat oil in a thick bottomed non stick pan and lay the chicken pieces in single layer in it. Grill on high heat, till the underside turns a reddish brown. Turn over and cook the other side similarly.
Reduce heat, drizzle some of the remaining marinade over the chicken pieces. Turn over and drizzle the remaining marinade, cover and cook, turning sides, till the chicken is fully cooked. Serve hot.