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 word-leading sensitivity to the stau mass (m_{\tilde{t}}
= 450GeV)
