Prepare the grill for direct cooking over medium-high heat (400° to 500°F).
Brush the cooking grates clean. Grill the bell peppers over direct medium-high heat, with the lid closed, until blackened all over, about 20 minutes, turning every 5 minutes. Transfer the peppers to a bowl, cover with plastic wrap, and let steam for 10 to 15 minutes.
Cut away the stem and core from each pepper, then slit each pepper lengthwise and remove the seeds and membranes. Peel away and discard the charred skin. Transfer the pepper to a food processor. Add the remaining marinade ingredients and process until smooth. Set aside a scant (¼ cup) for basting.
Arrange the chicken in a baking dish. Pour the remaining marinade over the chicken, rub some of the marinade between the skin and thighs and turn to coat. Cover with plastic wrap and refrigerate for at least 1 hour or up to 24 hours.
Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Grill the chicken, skin side up, over indirect medium heat, with the lid closed, until golden brown, about 30 minutes. Move to direct medium heat and continue to cook until the skin begins to crisp and an instant-read thermometer inserted into the thickest part of the chicken (not touching bone) registers 165°F, 6 to 10 minutes, turning occasionally and brushing with some of the reserved marinade. Remove from the heat and lightly season with salt and black pepper. Rest indoors for 3 to 5 minutes. Serve with lemon wedges.