The chin strap found on the Blue Service Cap that's worn with the Army Service/Dress Uniform is entirely ornamental. It was not designed or intended to be worn under either the chin or lower lip as a way of securing the cap in inclement conditions or while conducting ceremonial actions that might loosen the cap, and in point of fact the only personnel for these outcomes are a real threat are members of the Honor Guard, who are allowed to a wear a second, functional chin strap.
Note that this chin strap is designed for wear on Service Caps worn by enlisted personnel, up to and including the Sergeant Major of the Army.