Geo-neutrinos, electron anti-neutrinos produced in β decays of naturally occurring radioactive isotopes in the Earth, are a unique direct probe of our planet's interior. We report the first observation at more than 3σ C.L. of geo-neutrinos, performed with the Borexino detector at Laboratori Nazionali del Gran Sasso. Anti-neutrinos are detected through the neutron inverse β decay reaction. With a 252.6 ton yr fiducial exposure after all selection cuts, we detected 9.9+4.1-3.4(+14.6-8.2) geo-neutrino events, with errors corresponding to a 68.3% (99.73%) C.L. From the lnL profile, the statistical significance of the Borexino geo-neutrino observation corresponds to a 99.997% C.L. Our measurement of the geo-neutrinos rate is 3.9+1.6-1.3(+5.8-3.2...