Prepare grill for indirect grilling. If using a gas grill, heat one side to medium-high and leave one side with no heat. If using a charcoal grill, arrange hot coals on either side of charcoal grate, leaving an empty space in the middle.
Combine mango jam, chives, vinegar, and Sriracha, stirring until smooth. Reserve 1/4 cup mango mixture; set aside.
Brush oil evenly over chicken. Sprinkle chicken with salt and pepper.
Carefully remove grill rack. Place a disposable aluminum foil pan on unheated part of grill. Carefully return grill rack to grill. Place chicken on grill rack over unheated part. Brush chicken with about 2 tablespoons remaining mango mixture. Close lid; grill 90 minutes or until a thermometer inserted into meaty part of thigh registers 165°, turning chicken and brushing with about 2 tablespoons mango mixture every 20 minutes. Transfer the chicken to a platter. Drizzle chicken with reserved 1/4 cup mango mixture.