  We analyze the prospects of the detection of a $\mathcal{O}(1)$ GeV
neutralino dark matter, $\widetilde{\chi}^0_{1}$, in the Next-to-Minimal
Supersymmetric Standard Model at the 14 TeV LHC. We perform dedicated scans of
the relevant parameter space of the model and find a large number of points
where the thermal relic abundance due to such a dark matter is consistent with
the PLANCK measurement. We note that this dark matter is highly
singlino-dominated and is always accompanied by a pseudoscalar, $A_1$, with a
mass around twice its own, which is responsible for its resonant annihilation.
For two benchmark points from our scan, we then carry out a detector-level
signal-to-background analysis of the pair production of a heavier higgsino
neutralino and a chargino. The higgsino thus produced decays into the dark
matter and either the $Z$ boson or the $A_1$. For the $Z$-associated production
of $\widetilde{\chi}^0_{1}$, we investigate the scope of the trilepton search
channel. For the $A_1$-associated production mode, in order to identify the two
collimated muons coming from the decay of the $A_1$, we employ an
unconventional method of clustering them together into one jet-like object.
Using this method, for certain parameter space configurations, a much larger
sensitivity can be obtained at the 14 TeV LHC for the
$A_1\widetilde{\chi}^0_{1}$ channel compared to the $Z\widetilde{\chi}^0_{1}$
channel, with an integrated luminosity of 300 fb$^{-1}$.
