2 Tbsp. extra-virgin olive oil
3 garlic cloves, crushed
6 Tbsp. double-concentrated tomato paste
½ cup pure maple syrup
¼ cup soy sauce
¼ cup Worcestershire sauce
2 Tbsp. unseasoned rice vinegar
4 tsp. Sriracha or other hot sauce
Vegetable oil (for grill)
1 (3½–4-lb.) whole chicken, cut into 6–8 pieces, or whatever bone-in cut of chicken you feel like cooking
Heat olive oil in a small saucepan over medium. Cook garlic, turning occasionally, until golden brown, about 4 minutes. Add tomato paste and cook, stirring constantly and scraping bottom of pan, until slightly darkened, about 3 minutes. Add maple syrup, soy sauce, Worcestershire sauce, vinegar, and Sriracha. Bring to a boil, then reduce heat to medium-low and simmer until flavors have come together, about 1 minute. Remove from heat. Transfer about half of barbecue sauce to a heatproof bowl and set aside for serving.
Prepare a grill for medium-high indirect heat (for a charcoal grill, bank coals on one side of grill; for a gas grill, leave one or two burners off); oil grate. Season chicken generously with salt. Grill chicken over direct heat, turning every minute, until browned on all sides, about 5 minutes. Move chicken over indirect heat. Cover, positioning vent (if your grill has one) over chicken, and continue to grill, keeping grill covered as much as possible and turning every 5 minutes or so, until an instant-read thermometer inserted into thickest part registers 140°F–145°F, 18–25 minutes depending on the size of the pieces. Baste chicken with barbecue sauce and grill, turning and basting occasionally, until an instant-read thermometer inserted into thickest part registers 160°F for breast and 165°F for dark meat, about 10 minutes longer.
Arrange chicken on a platter. Serve with reserved barbecue sauce alongside.