The Virgo experiment, located near Pisa, Italy, is a large laser Michelson interferometer aiming at the first direct detection of gravitational waves. The interferometer monitors the relative distance of its mirrors placed at the ends of two 3 km-long perpendicular arms. The goal is to measure spectral differential variations of the arm lengths of 10−18 m/Hz1/2 in the frequency range from 10 Hz to 10 kHz. Avoiding spurious motions of the optical components is therefore essential to detect gravitational waves. Since the ground motion is 9 orders of magnitude larger than the arm length variations induced by gravitational waves, the seismic noise is the dominant low frequency noise source for terrestrial gravitational wave interferometers. The seismic isolation is obtained suspending the mirrors by an 8-meter tall chain of cascaded mechanical filters, called "Superattenuator" (SA). The Superattenuator is a passive device acting as a low pass filter in all six degrees of freedom, capable of attenuating the ground motion by more than 10 orders of magnitude, starting from a few Hz. To further reduce the seismic disturbances, the filter chain is suspended from an actively stabilized platform that compensates for low frequency and large amplitude oscillations caused by the mechanical resonances of the chain. In this article we describe the Superattenuator together with its control system, and we report about its performance.