Grind marinade ingredients into a paste and rub into chicken. Put on a rack and grill under high heat (or on a BBQ) until the skin is charred in places, turn and repeat in other side. While this is happening make the sauce.
Chop the spice paste ingredients (shallots, chilli, ginger, sugar, tamarind) and blend finely in a mortar and pestle (or food processor). Heat oil in a pot and fry the spice paste for 3-4 minutes until fragrant. Add coconut milk and simmer, stirring, until reduced by half. Season with salt and cook for 5-7 minutes until sauce thickens.
Coat each piece of grilled chicken in the sauce and then finish cooking it by roasting at 250 C for 30 minutes, or until cooked through. Baste a few times with more sauce as it cooks if you can be bothered or bring remaining sauce to simmer in pot and serve alongside chicken when cooked.