  We present the first comprehensive study of a giant, $\approx \! \! 70$
kpc-scale nebula around a radio-quiet quasar at $z<1$. The analysis is based on
deep integral field spectroscopy with MUSE of the field of HE$\,$0238$-$1904, a
luminous quasar at $z=0.6282$. The nebula emits strongly in $\mathrm{[O \,
II]}$, $\rm H \beta$, and $\mathrm{[O \, III]}$, and the quasar resides in an
unusually overdense environment for a radio-quiet system. The environment
likely consists of two groups which may be merging, and in total have an
estimated dynamical mass of $M_{\rm dyn}\approx 4\times 10^{13}$ to $10^{14}\
{\rm M_\odot}$. The nebula exhibits largely quiescent kinematics and irregular
morphology. The nebula may arise primarily through interaction-related
stripping of circumgalactic and interstellar medium (CGM/ISM) of group members,
with some potential contributions from quasar outflows. The simultaneous
presence of the giant nebula and a radio-quiet quasar in a rich environment
suggests a correlation between such circum-quasar nebulae and environmental
effects. This possibility can be tested with larger samples. The upper limits
on the electron number density implied by the $\mathrm{[O \, II]}$ doublet
ratio range from $\log(n_{\rm e, \, [O \, II]} / \mathrm{cm^{-3}}) < 1.2$ to
$2.8$. However, assuming a constant quasar luminosity and negligible projection
effects, the densities implied from the measured line ratios between different
ions (e.g., $\mathrm{[O\,II]}$, $\mathrm{[O\,III]}$, and $\mathrm{[Ne\,V]}$)
and photoionization simulations are often $10{-}400$ times larger. This large
discrepancy can be explained by quasar variability on a timescale of $\approx
10^4{-}10^5$ years.
