PSR B1951+32 is a gamma-ray pulsar detected by the Energetic Gamma Ray Experiment Telescope (EGRET) identified with the 39.5 ms radio pulsar in the supernova remnant CTB 80. The pulsar energy spectrum is consistent with an unbroken power law with exponent -1.74 +/- 0.11 between 100 MeV and 30 GeV with a peak in energy output somewhere beyond 30 GeV. Here we report on the first observations of PSR B1951+32 beyond 30 GeV. The observations were carried out with the 10m gamma-ray telescope at the Whipple Observatory on Mt. Hopkins, Arizona. In 8.1 hours of observation we find no evidence for steady or periodic emission from PSR B1951+32 above ~ 260 GeV. Flux upper limits are derived and compared with model extrapolations from lower energies and the predictions of emission models.