We have converted the former solar electrical plant THEMIS (French Pyrenees) into an atmospheric Cherenkov detector called CELESTE, which records gamma rays above 30 GeV (7E24 Hz). Here we present the first sub-100 GeV detection by a ground based telescope of a gamma ray source, the Crab nebula, in the energy region between satellite measurements and imaging atmospheric Cherenkov telescopes. At our analysis threshold energy of 60 +/- 20 GeV we measure a gamma ray rate of 6.1 +/- 0.8 per minute. Allowing for 30% systematic uncertainties and a 30% error on the energy scale yields an integral gamma ray flux of I(E>60 GeV) = 6.2^{+5.3}_{-2.3} E-6 photons m^-2 s^-1. The analysis methods used to obtain the gamma ray signal from the raw data are detailed. In addition, we determine the upper limit for pulsed emission to be <12% of the Crab flux at the 99% confidence level, in the same energy range. Our result indicates that if the power law observed by EGRET is attenuated by a cutoff of form e^{-E/E_0} then E_0 < 26 GeV. This is the lowest energy probed by a Cherenkov detector and leaves only a narrow range unexplored beyond the energy range studied by EGRET. Comment: 34 pages, accepted by the Astrophysical Journal