We report the results of the first search for gravitational waves from compact binary coalescence using data from the LIGO and Virgo detectors. Five months of data were collected during the concurrent S5 (LIGO) and VSR1 (Virgo) science runs. The search focused on signals from binary mergers with a total mass between 2 and 35 Msun. No gravitational waves are identified. The cumulative 90%-confidence upper limits on the rate of compact binary coalescence are calculated for non-spinning binary neutron stars, black hole-neutron star systems, and binary black holes to be 8.7x10^-3, 2.2x10^-3 and 4.4x10^-4 yr^-1 L_10^-1 respectively, where L_10 is 10^10 times the blue solar luminosity. These upper limits are compared with astrophysical expectations.
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