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 1×10(32) cm-2 s-1, an integrated luminosity of 10 pb-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 mg - mχ1(0) >100 GeV/c2, and assuming BR(g→gχ1(0))=100%, mg < 370 GeV/c2 are excluded for lifetimes from 10 μs to 1000 s.