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The bright gamma-ray source. Geminga has been identified as an X-ray and gamma-ray pulsar with a pulse period of 237 ms. Geminga was observed with the University of Durham very high-energy (VHE) gamma-ray telescopes at Dugway, Utah, in 1983. The analysis of these data has revealed pulsations at the X-ray/gamma-ray pulse period, with the VHE gamma-ray pulses being in phase with the lower-energy gamma-ray pulses. The VHE and HE gamma-ray light curves are connected with a significance for positive correlation of 6* 10-4. The VHE gamma-ray signal corresponds to a flux of about 3* 10-11 cm-2 s-1 at energies greater than 1000 GeV, and a luminosity of 6* 10 30 erg s-1.