It was shown in a previous study that a lightest neutralino with mass below 30 GeV was severely constrained in the minimal supersymmetric standard model (MSSM), unless it annihilates via a light stau and thus yields the observed dark matter abundance. In such a scenario, while the stau is the next-to-lightest supersymmetric particle (NLSP), the charginos and the other neutralinos as well as sleptons of the first two families are also likely to be not too far above the mass bounds laid down by the Large Electron Positron (LEP) collider. As the branching ratios of decays of the charginos and the next-to-lightest neutralino into staus are rather large, one expects significant rates of tau-rich final states in such a case. With this in view, we investigate the same-sign ditau and tri-tau signals of this scenario at the Large Hadron Collider (LHC) for two MSSM benchmark points corresponding to light neutralino dark matter. The associated signal rates for these channels are computed, for the centre-of-mass energy of 14 TeV. We find that both channels lead to appreciable rates if the squarks and the gluino are not too far above a TeV, thus allowing to probe scenarios with light neutralinos in the 14 TeV LHC run with 10-100 fb^{-1}.