Just to reiterate, sate / satay is the dish, not the peanut sauce. There is an entire post dedicated to that topic; go read it for better understanding of the dish.If grilling over live coal, soak the bamboo skewers in water for at least 30 minutes to lessen the chance that they will catch fire on the grill.
Pound the chicken fillets into uniform thickness then cut into bite size pieces.
Place the chicken pieces in a bowl, add the rest of the ingredients for the marinade and mix well.
Cover the bowl and let the chicken soak up the flavors for 30 minutes in the fridge.
Make the peanut dipping sauce
While the chicken marinates, whisk the lime juice sugar and fish sauce in a microwaveable bowl.
Add the peanut butter and ginger to the lime-sugar-fish sauce mixture.
Microwave for 10 seconds on HIGH to soften the peanut butter.
Stir in the sesame seed oil.
Taste and add more lime juice, fish sauce or sugar, until you get the balance that pleases you.
Grill the chicken
Drain the chicken.
Thread the chicken pieces with the bamboo skewers, three to five pieces per skewer depending on their length.
Grill the skewered chicken (charcoal is traditional but we did this on a stovetop grill) over medium-high heat, two to four minutes per side depending on the thickness of the meat.
Serve the chicken sate / satay
Arrange the grilled skewered chicken on a plate and serve with peanut dipping sauce on the side.