In models of anomaly-mediated supersymmetry breaking (AMSB), the lightest chargino is predicted to have a lifetime long enough to be detected in collider experiments. This letter explores AMSB scenarios in pp collisions at root s = 7 TeV by attempting to identify decaying charginos which result in tracks that appear to have few associated hits in the outer region of the tracking system. The search was based on data corresponding to an integrated luminosity of 1.02 fb(-1) collected with the ATLAS detector in 2011. The p(T) spectrum of candidate tracks is found to be consistent with the expectation from Standard Model background processes and constraints on the lifetime and the production cross section were obtained. In the minimal AMSB framework with m(3/2) < 32 TeV, m(0) < 1.5 TeV, tan beta = 5 and mu > 0, a chargino having mass below 92 GeV and a lifetime between 0.5 ns and 2 ns is excluded at 95 % confidence level.