A stochastic background of gravitational waves is expected to arise from a superposition of many incoherent sources of gravitational waves, of either cosmological or astrophysical origin. This background is a target for the current generation of ground-based detectors. In this article we present the first joint search for a stochastic background using data from the LIGO and Virgo interferometers. In a frequency band of 600-1000 Hz, we obtained a 95% upper limit on the amplitude of $\Omega_\text{GW}(f)=\Omega_3(f/900\text{ Hz})^3$, of $\Omega_3<0.32$, assuming a value of the Hubble parameter of $h_{100}=0.71$. These new limits are a factor of seven better than the previous best in this frequency band.