This thesis presents a search for evidence of new supersymmetric particles in proton-proton collision data collected by the Compact Muon Solenoid at the Large Hadron Collider located in Geneva, Switzerland. The data was collected in 2012 at a center of mass energy of 8 TeV and corresponds to an integrated luminosity of 19.5 inverse femtobarns. The search examines events that produce the experimental signature of a disappearing track. Disappearing tracks are identifed as those with little or no associated calorimeter energy deposits and with several missing hits in the outer layers of the tracker. This search is motived by anomaly-mediated supersymmetry which postulates that a long-lived chargino decaying to a neutralino and pion with low momentum could give rise to a disappearing track. The sources of background in this search arise from leptons which fail to be reconstructed and false trajectories determined by the track reconstruction algorithm. The number of observed events is in agreement with the background expectation, and limits are set on the cross section of direct electroweak chargino production in terms of the chargino mass and mean proper lifetime. At 95 % confidence level, anomaly-mediated supersymmetry breaking models with a chargino mass less than 260 GeV, corresponding to a mean proper lifetime of 0.2 ns, are excluded.