We analyze the encounters of the neutron star 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 kms-1
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 of ≈25 pc from the center of the compact OB association λ Ori at about t = -0.39 Myr, which is close to the age of the pulsar estimated from its timing.