Many extensions of the Standard Model predict the existence of charged heavy long-lived particles, such as R-hadrons or charginos. These particles, if produced at the Large Hadron Collider, should be moving non-relativistically and are therefore identifiable through the measurement of an anomalously large specific energy loss in the ATLAS pixel detector. Measuring heavy long-lived particles through their track parameters in the vicinity of the interaction vertex provides sensitivity to metastable particles with lifetimes from 0.6 ns to 30 ns. A search for such particles with the ATLAS detector at the Large Hadron Collider is presented, based on a data sample corresponding to an integrated luminosity of  fb of pp collisions at  TeV. No significant deviation from the Standard Model background expectation is observed, and lifetime-dependent upper limits on R-hadrons and chargino production are set. Gluino R-hadrons with 10 ns lifetime and masses up to 1185 GeV are excluded at 95  confidence level, and so are charginos with 15 ns lifetime and masses up to 482 GeV.