To prepare saté, combine chicken and next 6 ingredients (through 2 garlic cloves) in a medium bowl. Let stand 10 minutes.
To prepare sauce, combine 1 tablespoon brown sugar and the next 5 ingredients (through 1 garlic clove) in a medium bowl, stirring until sugar dissolves.
Thread chicken strips onto each of 8 (8-inch) skewers. Place chicken on grill rack coated with cooking spray; grill 5 minutes on each side or until chicken is done. Serve chicken with sauce.