THE strong γ-ray source Geminga was first observed by the satellite SAS-21,2 and later seen by the COS-B satellite3,4. An association with the peculiar X-ray source 1E0630 + 178 was proposed5, suggesting that Geminga is a nearby neutron star (~100 pc from Earth) which is not visible as a radio pulsar. Searches for its optical counterpart yielded as the best candidate a very faint (mv=25.5) object, G'', which was proposed on the basis of its colours6-8. The association of Geminga with 1E0630+178 was confirmed recently by the discovery of a 237-ms periodicity in the soft X-ray emission9 from the latter; such oscillations were recognized immediately afterwards in data10 from the Gamma Ray Observatory, and in reanalysis of the COS-B11 and SAS-2 data12. As its timing and energy parameters indicated that Geminga is closer than 400 pc, Bignami and Caraveo suggested11 that the proper motion of the optical counterpart G'' might be measurable. Here we compare a 1992 optical image of G'' with previous data from 1984 and 1987, and find that the proper motion is 0.17 arcsec per year. This motion is consistent with the identification of G'' as a neutron star at a distance of about 100 pc, thus confirming it as the optical counterpart of Geminga.