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TAIGA-HiSCORE is a Cherenkov shower-front timing array, that operates at the Tunka site in Siberia. It is part of the hybrid TAIGA facility for cosmic-ray and gamma-ray physics, that is currently under construction. TAIGA-HiSCORE is today a 0.25km2 detector array comprising 28 optical detector stations with 0.6 sr acceptance and a detection threshold for extended air shower of several 10's of TeV each. It will be upgraded to 60 stations on 0.6 km2 by fall 2017. HiSCORE operated over the winter-seasons 2015/16 and 2016/17 in moonless, clear nights to detect cosmic ray and gamma ray shower. As a serendipitous discovery, it detected a first, fast moving point source : the LIDAR of the Cloud-Aerosol Transport System (CATS), operating onboard the International Space Station (ISS), with a focused beam at 532nm pointing nearly vertically downward. During the ~1 sec ISS near-zenith passages, we detect large amplitude pulses on the HiSCORE stations, with the 4 kHz LIDAR repetition rate and few nsec duration. A directional reconstruction of the light direction, based on photon arrival times, points back to the ISS at ~400km height. In addition, a number of the ISS-generated light pulses are found to arrive from directions very different from the ISS, being compatible with LIDAR light scattered in clouds. We discuss characteristics of the light signals detected during ISS passages, which are strikingly different from air shower events with a curved shower front. We use them to verify time calibration and directional reconstruction precision, as well as absolute pointing of the TAIGA-HiSCORE array.