  We present the detection of excited fine-structure energy levels of
singly-ionized silicon and neutral carbon associated with the proximate damped
Lyman-$\alpha$ system at $z_{\rm abs}=2.811$ towards \qso. This absorber has an
apparent relative velocity that is inconsistent with the Hubble flow indicating
motion along the line-of-sight towards the quasar, i.e., $z_{\rm abs}>z_{\rm
em}$. We measure the metallicity of the system to be ${\rm [Zn/H]}=-0.68\pm
0.02$. Using the relative populations of the fine-structure levels of SiII and
CI, as well as the populations of H$_2$ rotational levels, we constrain the
physical conditions of the gas. We derive hydrogen number densities of $n_{\rm
H}=190^{+70}_{-50}$ cm$^{-3}$ and $260^{+30}_{-20}$ cm$^{-3}$ in two velocity
components where both CI and H$_2$ are detected. Taking into account the
kinetic temperature in each component, $\sim 150$K, we infer high values of
thermal pressure in the cold neutral medium probed by the observations. The
strengths of the UV field in Draine's unit are $I_{\rm UV} = 10^{+5}_{-3}$ and
$14^{+3}_{-3}$ in each of these two components, respectively. Such enhanced UV
fluxes and thermal pressure compared to intervening DLAs are likely due to the
proximity of the quasar. The typical size of the absorber is $\sim 10^4$ a.u.
Assuming the UV flux is dominated by the quasar, we constrain the distance
between the quasar and the absorber to be $\sim 150-200$ kpc. This favours a
scenario where the absorption occurs in a companion galaxy located in the group
where the quasar-host galaxy resides. This is in line with studies in emission
that revealed the presence of several galaxies around the quasar.
