The measurement of the space-time structure variations induced by strong cosmic events (supernovae, coalescing binaries of neutron stars, etc.) requires an oscillator with a relative stability of 10 -21 on time scales typically ≈100 ms. We demonstrate that the Virgo interferometer with a wavelength of 1.064 μm has a laser frequency with an in-loop stability of 1.0 × 10 -21 on a 100 ms time scale, and an in-loop frequency noise of 2 × 10 -7 Hz/√Hz at 10 Hz. We show that this fits the specifications. Two references successively stabilize the laser frequency. The first one is a 144 m long suspended cavity; the second one is the common mode of two perpendicular 3 km long Fabry-Perot cavities. The differential mode of the relative length variations of these two optical cavities is the port where we expect the signal for the gravitational waves; this out-of-loop measurement, less sensitive to laser frequency noise, does not show up correlations with the in-loop error signal. This is the best ever performance of short term laser frequency stabilization reported.