New metastable massive particles with electric and colour charge are features of many theories beyond the Standard Model. A search is performed for long-lived gluino-based R-hadrons with the ATLAS detector at the LHC using a data sample corresponding to an integrated luminosity of 31 pb(-1). We search for evidence of particles that have come to rest in the ATLAS detector and decay at some later time during the periods in the LHC bunch structure without proton-proton collisions. No significant deviations from the expected backgrounds are observed, and a cross-section limit is set. It can be interpreted as excluding gluino-based R-hadrons with masses less than 341 GeV at the 95 % C.L., for lifetimes from 10(-5) to 10(3) seconds and a neutralino mass of 100 GeV.