  TUS (Tracking Ultraviolet Set-up) is the world's first orbital detector of
ultra-high-energy cosmic rays (UHECRs). It was launched into orbit on 28th
April 2016 as a part of the scientific payload of the Lomonosov satellite. The
main aim of the mission was to test the technique of measuring the ultraviolet
fluorescence and Cherenkov radiation of extensive air showers generated by
primary cosmic rays with energies above ~100 EeV in the Earth atmosphere from
space. During its operation for 1.5 years, TUS registered almost 80,000 events
with a few of them satisfying conditions anticipated for extensive air showers
(EASs) initiated by UHECRs. Here we discuss an event registered on 3rd October
2016. The event was measured in perfect observation conditions as an
ultraviolet track in the nocturnal atmosphere of the Earth, with the kinematics
and the light curve similar to those expected from an EAS. A reconstruction of
parameters of a primary particle gave the zenith angle around 44$^\circ$ but an
extreme energy not compatible with the cosmic ray energy spectrum obtained with
ground-based experiments. We discuss in details all conditions of registering
the event, explain the reconstruction procedure and its limitations and comment
on possible sources of the signal, both of anthropogenic and astrophysical
origin. We believe this detection represents a significant milestone in the
space-based observation of UHECRs because it proves the capability of an
orbital telescope to detect light signals with the apparent motion and light
shape similar to what are expected from EASs. This is important for the
on-going development of the future missions KLYPVE-EUSO and POEMMA, aimed for
studying UHECRs from space.
