  We consider a Minimal Supersymmetric Standard Model scenario in which the
only light superparticles are a bino-like dark matter candidate and a
nearly-degenerate slepton. It is notoriously difficult to probe this scenario
at the Large Hadron Collider, because the slepton pair-production process
yields a final state with soft leptons and small missing transverse energy. We
study this scenario in the region of parameter space where the mass difference
between the lightest neutralino and the lightest slepton ($\Delta m$) is
$\lesssim 60~{\rm GeV}$, focusing on the process in which an additional
radiated jet provides a transverse boost to the slepton pair. We then utilize
the angular separation of the leptons from each other and from the missing
transverse energy, as well as the angular separation between the jet and the
missing transverse energy, to distinguish signal from background events. We
also use the reconstructed ditau mass, the $\cos \theta^*_{\ell^+ \ell^-}$
variable, and for larger $\Delta m$, a lower bound on the lepton $p_T$. These
cuts can dramatically improve both signal sensitivity and the
signal-to-background ratio, permitting discovery at the Large Hadron Collider
with reasonable integrated luminosity over the interesting region of parameter
space. Using our search strategy the LHC will be able to exclude
$m_{\tilde{\mu}} \approx 200$ GeV for $\Delta m \lesssim 60$ GeV at $1.5-3
\sigma$ with 1000 fb$^{-1}$ of integrated luminosity. Although we focus on a
particular model, the results generalize to a variety of scenarios in which the
dark matter and a leptonic partner are nearly degenerate in mass, and
especially to scenarios featuring a scalar mediator.
