  Although the Galactic supernova rate is about 2 per century, only few
supernova remnants are associated with historical records. There are a few
ancient Chinese records of "guest stars" that are probably sightings of
supernovae for which the associated supernova remnant is not established. Here
we present an X-ray study of the supernova remnant G7.7-3.7, as observed by
XMM-Newton, and discuss its probable association with the guest star of 386 CE.
This guest star occurred in the ancient Chinese asterism Nan-Dou, which is part
of Sagittarius. The X-ray morphology of G7.7-3.7 shows an arc-like feature in
the SNR south, which is characterized by an under-ionized plasma with sub-solar
abundances, a temperature of 0.4--0.8 keV, and a density of $\sim 0.5(d/4
kpc)^{-0.5}$ cm$^{-3}$. A small shock age of $1.2\pm 0.6 (d/4 kpc)^{0.5}$ kyr
is inferred from the low ionization timescale of $2.4^{+1.1}_{-1.3}\times
10^{10}$ cm$^{-3}$ s of the X-ray arc. The low foreground absorption
($N_H=3.5\pm0.5\times 10^{21}$ cm$^{-2}$) of G7.7-3.7 made the supernova
explosion visible to the naked eyes on the Earth. The position of G7.7-3.7 is
consistent with the event of 386 CE, and the X-ray properties suggest that also
its age is consistent. Interestingly, the association between G7.7-3.7 and
guest star 386 would suggest the supernova to be a low-luminosity supernova, in
order to explain the not very long visibility (2--4 months) of the guest star.
