Prepare grill for medium-high heat. Whisk brown sugar, vinegar, chili paste, fish sauce, Sriracha, and ginger in a large bowl. Add chicken and toss to coat. Thread 4 or 5 chicken pieces onto each skewer.
Transfer marinade to a small saucepan. Bring to a boil, reduce heat, and simmer until reduced by half (about 1 cup), 7–10 minutes.
Grill chicken, turning and basting often with reduced marinade, until cooked through, 8–10 minutes.
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