Place chicken on a rimmed baking sheet. Make spice rub: Combine all ingredients in a small bowl. Sprinkle spice mix over chicken and rub in. Cover with plastic wrap and chill for at least 6 hours.
Make sauce: Combine all ingredients in a large pan. Bring to a boil, stirring continuously. Simmer, uncovered, for 15 minutes, stirring occasionally, until thickened. Remove from heat.
Preheat grill to medium low; oil when hot. Cook chicken for 10 minutes, turn over and cook for 8 minutes longer. Brush sauce on one side of chicken, turn over and cook for 3 minutes. Brush remaining side with sauce, turn over and cook for 3 minutes, or until cooked through.