Combine all marinade ingredients in a mixing bowl and stir well.
Add the chicken parts or thighs, plus the red peppers. Stir well to ensure the chicken and peppers are covered with marinade.
Cover and place in the refrigerator while you prepare the dipping sauce. (Better yet, allow to marinate several hours, or overnight.)
To make the dipping sauce/glaze, place all the dipping sauce/glaze ingredients in a sauce pan. Stir and bring to a boil.
Reduce heat to medium-low. Allow sauce to simmer for 10-15 minutes, stirring occasionally. The sauce will thicken as it cooks and become tangy - a mixture of sweet, sour, salty, and spicy.
Tip: this sauce can be served warm, at room temperature, or cold. Also, it can easily be made it ahead of time and kept in the refrigerator until needed.
When sauce is done cooking, adjust it by adding more sugar if too sour for your taste, or more lime juice if too sweet.
Barbecue the chicken outdoors, OR follow these instructions for indoor cooking:
Leave the peppers in the bowl for now. Place chicken in a baking dish or on a baking sheet (one with "sides" to catch any drippings), or a broiling pan if you have one. Bake in the oven at 350 degrees for 40-45 minutes, or until chicken is nearly cooked (juices should run clear).
Now turn the oven on to "broil" setting. Remove chicken and brush with some of the leftover marinade. Also lay the red pepper alongside the chicken (if there's no room, use a separate pan).
Place the chicken and peppers on one of the higher racks of your oven (near the heating element) for 5 minutes, then pull out, turn the chicken and peppers, and continue broiling for another 5 minutes on the other side. Do this a couple of times, or until both the chicken and the peppers have that nice browned barbecued look.
If grilling the red peppers outdoors, simply barbecue the vegetables as you would meat, but turning them more often. Note that barbecued vegetables take only minutes to cook.
Serve the chicken with the dipping sauce on the side. OR spoon a little sauce over each piece of chicken as a glaze before serving. Add the roasted red peppers onto the side of the serving platter. Serve with Thai jasmine-scented rice.
Drinks: Serve with a cold lager or a chilled glass of your favorite white wine. ENJOY!!