For the first time, the optimized stellarator Wendelstein 7-X has operated with an island divertor. An operation regime in hydrogen was found in which the total plasma radiation approached the absorbed heating power without noticeable loss of stored energy. The divertor thermography recorded simultaneously a strong reduction of the heat load on all divertor targets, indicating almost complete power detachment. This operation regime was stably sustained over several energy confinement times until the preprogrammed end of the discharge. The plasma radiation is mainly due to oxygen and is located at the plasma edge. This plasma scenario is reproducible and robust at various heating powers, plasma densities, and gas fueling locations. These experimental results show that the island divertor concept actually works and displays good power dissipation potential, producing a promising exhaust concept for the stellarator reactor line.