  We analyze the encounters of the neutron star (pulsar) Geminga with open star
clusters in the OB association OriOB1a through the integration of epicyclic
orbits into the past by taking into account the errors in the data. The open
cluster ASCC21 is shown to be the most probable birthplace of either a single
progenitor star for the Geminga pulsar or a binary progenitor system that
subsequently broke up. Monte Carlo simulations of Geminga--ASCC21 encounters
with the pulsar radial velocity Vr =-100+-50 km/s have shown that close
encounters could occur between them within <= 10 pc at about t=-0.52 Myr. In
addition, the trajectory of the neutron star Geminga passes at a distance about
25 pc from the center of the compact OB association lambda Ori at about t=-0.39
Myr, which is close to the age of the pulsar estimated from its timing.
