  We demonstrate that megaton-mass neutrino telescopes are able to observe the
signal from long-lived particles beyond the Standard Model, in particular the
stau, the supersymmetric partner of the tau lepton. Its signature is an excess
of charged particle tracks with horizontal arrival directions and energy
deposits between 0.1 and 1 TeV inside the detector. We exploit this
previously-overlooked signature to search for stau particles in the publicly
available IceCube data. The data shows no evidence of physics beyond the
Standard Model. We derive a new lower limit on the stau mass of $320$ GeV (95\%
C.L.) and estimate that this new approach, when applied to the full data set
available to the IceCube collaboration, will reach world-leading sensitivity to
the stau mass ($m_{\tilde{\tau}}=450\,\mathrm{GeV}$).
