The results of the first search for long-lived gluinos produced in 7 TeV pp collisions at the CERN Large Hadron Collider are presented. The search looks for evidence of long-lived particles that stop in the CMS detector and decay in the quiescent periods between beam crossings. In a dataset with a peak instantaneous luminosity of 1×1032cm-2s-1, an integrated luminosity of 10pb-1, and a search interval corresponding to 62 hours of LHC operation, no significant excess above background was observed. Limits at the 95% confidence level on gluino pair production over 13 orders of magnitude of gluino lifetime are set. For a mass difference m g-mχ10>100GeV/c2, and assuming BR(g→gχ10)= 100%, mg<370GeV/c2 are excluded for lifetimes from 10μs to 1000 s. © 2010 The American Physical Society.