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 $\Omega_{\rm GW}(f) = \Omega_3 (f/900
\mathrm{Hz})^3$, of $\Omega_3 < 0.33$, assuming a value of the Hubble parameter
of $h_{100}=0.72$. These new limits are a factor of seven better than the
previous best in this frequency band.
