We report the successful in situ measurement of interstellar dust particles inside the orbit of the Earth with the Cosmic Dust Analyzer (CDA) on the Cassini spacecraft. The impact ionization subsystem of the CDA is similar to the instruments on Ulysses and Galileo. As the heliocentric velocity and the direction of the interstellar dust flux are well known from Ulysses measurements, a combined analysis of the impact charge signals together with geometric and kinematic spacecraft data allowed us to separate interplanetary impacts from interstellar ones. The mean interstellar flux between 0.7 and 1.2 AU derived from our analysis is 2.5 ¿ 0.5 ¿ 10-5 m-2s-1, in a mass range of 5 ¿ 10-17 kg to 10-15 kg which is in good agreement with the interstellar dust flux measured by Ulysses at 3 AU during the same time period <Landgraf et al., 2003>. The simultaneous detection of interstellar grains by Ulysses at 3 AU and approximately 1 AU by Cassini proves that big interstellar grains (radius greater than 0.4 ¿m), can penetrate deeply into the inner solar system.