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 $1\ifmmode\times\else\texttimes\fi{}{10}^{32}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, an integrated luminosity of $10\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$, 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 ${m}_{\stackrel{\texttildelow{}}{g}}\ensuremath{-}{m}_{{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}}>100\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, and assuming $\mathrm{BR}(\stackrel{\texttildelow{}}{g}\ensuremath{\rightarrow}g{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0})=100%$, ${m}_{\stackrel{\texttildelow{}}{g}}<370\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ are excluded for lifetimes from $10\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ to 1000 s.