INTEGRAL has observed 47 long-duration GRBs (T_90 > 2s) and 1 short-duration GRB (T_90 < 2s) in five years of observation since October 2002. This work presents the properties of the prompt emission of GRB 070707, which is the first short hard GRB observed by INTEGRAL. The spectral and temporal properties of GRB 070707 were determined using the two sensitive coded-mask gamma-ray instruments on board INTEGRAL, IBIS and SPI. The T_90 duration was 0.8s, and the spectrum of the prompt emission was obtained by joint deconvolution of IBIS and SPI data to yield a best fit power-law with photon index alpha = -1.19 +0.14 -0.13, which is consistent with the characteristics of short-hard gamma-ray bursts. The peak flux over 1 second was 1.79 photons/cm^2/s and the fluence over the same interval was 2.07 x 10^-7 erg/cm^2 in the energy range 20-200keV. The spectral lag measured between 25-50keV and 100-300keV is 20 +/- 5ms, consistent with the small or negligible lags measured for short bursts. The spectral and temporal properties of GRB 070707 are comparable to those of the short hard bursts detected by other gamma-ray satellites, including BATSE and Swift. We estimate a lower limit on the Lorentz factor Gamma >~ 25 for GRB 070707, assuming the typical redshift for short GRBs of z=0.35. This limit is consistent with previous estimates for short GRBs and is smaller than the lower limits of Gamma >~ 100 calculated for long GRBs. If GRB 070707 is a member of the recently postulated class of short GRBs at z ~ 1, the lower limit on Gamma increases to Gamma >~ 35.
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