We report the observation of anomalous multimuon events produced at the Fermilab Tevatron collider and recorded by the CDF II detector. In a data set acquired with a dedicated dimuon trigger and corresponding to an integrated
luminosity of 2100 pb−1, we isolate a sample of events in which the identified muons have extremely large impact parameters. Within these events, the muon multiplicity is also anomalously large. We are unable to explain these events through standard model processes in conjunction with our current understanding of the CDF II detector, trigger and event reconstruction. In addition to describing the analysis, we explore a conjecture of new physics that is manifestly suggested by the topology and kinematical properties of these events