For the sauce: Preheat half of a grill to 400 degrees F. Using an upside-down wire cooling rack or a grill basket over the direct-heat side of the grill, add the tomatoes, Thai bird chiles, onions, bell peppers and jalapeno peppers. Roast, tossing and flipping until everything is charred, 20 to 25 minutes.
Boil vegetables: Add the charred vegetables to a medium pot along with the vinegar, sugar, garlic, a pinch of salt and enough water to just cover the vegetables. Bring to a boil over high heat, then lower and let simmer, stirring occasionally, until the liquid is reduced by half, 15 to 20 minutes. Remove from the heat and allow to cool, then blend until smooth. Pass the sauce through a fine-mesh strainer.
For the chicken: Add the chicken, 1/2 cup sauce and vegetable oil to a large resealable bag. Mix and seal, then marinate for 1 to 2 hours at room temperature.
Preheat half of a grill to 400 degrees F.
Remove chicken from bag, discard marinade and pat chicken dry. Place chicken, smooth-side down, over direct heat to char, then flip and finish cooking over indirect heat for a total of 10 to 15 minutes depending on piece and heat. Brush the chicken with sauce the last few minutes of grilling. Serve with more sauce on the side.