Put all the marinade ingredients (except the chicken!) into a food processor and blend into a paste.
Using a sharp knife, make 2-3 deep slashes into each chicken drumstick. This will help the marinade permeate and create better flavour.Either in a bowl or a plastic resealable bag mix together the marinade and chicken. Make sure all the chicken gets a good coating. Cover the bowl or seal the bag and refrigerate for as long as you can. 4-5 hours minimum or 24 hours for the tastiest results.
Remove from the fridge about 1 hour before you plan to cook. Heat your BBQ grill or a hot oven grill.Grill the chicken for about 10-15 minutes, turning regularly - baste the chicken with some of the leftover marinade for added flavour. You want a nice char on the outside - it's all flavour!
Let the chicken rest for 5 minutes, then serve. I like to serve mine with a spicy dipping sauce like nam jim jaew (details and recipe for that below in the notes).