  The near-Earth (within $\sim 100$ pc) supernova explosions in the past
several million years can cause the global deposition of radioactive elements
(e.g., $^{60}$Fe) on Earth. The remnants of such supernovae are too old to be
easily identified. It is therefore of great interest to search for
million-year-old near-Earth neutron stars or black holes, the products of
supernovae. However, neutron stars and black holes are challenging to find even
in our Solar neighbourhood if they are not radio pulsars or X-ray/$\gamma$-ray
emitters. Here we report the discovery of one of the nearest ($127.7 \pm 0.3$
pc) neutron star candidates in a detached single-lined spectroscopic binary
LAMOST J235456.73+335625.9 (hereafter J2354). Utilizing the time-resolved
ground-based spectroscopy and space photometry, we find that J2354 hosts an
unseen compact object with $M_{\mathrm{inv}}$ being $1.4 \sim 1.6\ M_{\odot}$.
The follow-up Swift ultraviolet (UV) and X-ray observations suggest that the UV
and X-ray emission is produced by the visible star rather than the compact
object. Hence, J2354 probably harbours a neutron star rather than a hot
ultramassive white dwarf. Two-hour exceptionally sensitive radio follow-up
observations with Five-hundred-meter Aperture Spherical radio Telescope fail to
reveal any pulsating radio signals at the $6\sigma$ flux upper limit of $12.5\
\mu \mathrm{Jy}$. Therefore, the neutron star candidate in J2354 can only be
revealed via our time-resolved observations. Interestingly, the distance
between J2354 and our Earth can be as close as $\sim 50$ pc around $2.5$ Myrs
ago, as revealed by the Gaia kinematics. Our discovery demonstrates a promising
way to unveil the hidden near-Earth neutron stars in binaries by exploring the
optical time domain, thereby facilitating understanding of the metal-enrichment
history in our Solar neighbourhood.
