The blazar 1ES 1959+650 was observed in a flaring state with the Whipple 10 m Imaging Atmospheric Cerenkov Telescope in 2002 May. A spectral analysis has been carried out on the data from that time period, and the resulting very high energy gamma-ray spectrum (E ≥ 316 GeV) can be well fitted by a power law of differential spectral index α = 2.78 ± 0.12stat ± 0.21sys. On 2002 June 4, the source flared dramatically in the gamma-ray range without any coincident increase in the X-ray emission, providing the first unambiguous example of an “orphan” gamma-ray flare from a blazar. The gamma-ray spectrum for these data can also be described by a simple power-law fit with α = 2.82 ± 0.15stat ± 0.30sys. There is no compelling evidence for spectral variability or for any cutoff to the spectrum.