An anti-skid device for vehicle tires is provided which includes a chain cover formed by two spaced apart chain lengths (9) formed of links (11), that are connected by connector links (15). Guide chain bodies (23) engage the connector links (15), which connect the chain cover to retainer loops (29) arranged in a star-shaped pattern on the vehicle wheel. The connection between the retainer loops (29) and the chain cover is achieved by a single guide chain body (23) and results in a uniform usage of all elements over the entire circumference. The chain cover can be turned over by undoing the guide chain bodies (23).