Abstract: Many extensions of the Standard Model posit the existence of heavy particles with long lifetimes. In this Letter, results are presented of a search for events containing one or more such particles, which decay at a significant distance from their production point, using a final state containing charged hadrons and an associated muon. This analysis uses a data sample of proton-proton collisions at root s = 7 TeV corresponding to an integrated luminosity of 4.4 fb(-1) collected in 2011 by the ATLAS detector operating at the Large Hadron Collider. Results are interpreted in the context of R-parity violating supersymmetric scenarios. No events in the signal region are observed and limits are set on the production cross section for pair production of supersymmetric particles, multiplied by the square of the branching fraction for a neutralino to decay to charged hadrons and a muon, based on the scenario where both of the produced supersymmetric particles give rise to neutralinos that decay in this way. However, since the search strategy is based on triggering on and reconstructing the decay products of individual long-lived particles, irrespective of the rest of the event, these limits can easily be reinterpreted in scenarios with different numbers of long-lived particles per event. The limits are presented as a function of neutralino lifetime, and for a range of squark and neutralino masses.