The magnetic behavior of the Ca3Co2O6 spin chain compound is characterized by a large Ising-like character of its ferromagnetic chains, set on triangular lattice, that are antiferromagnetically coupled. At low temperature, T < 7K, the 3D antiferromagnetic state evolves towards a spin frozen state. In this temperature range, magnetic field driven magnetization of single crystals (H//chains) exhibits stepped variations. The occurrence of these steps at regular intervals of the applied magnetic field, Hstep=1.2T, is reminiscent of the quantum tunneling of the magnetization (QTM) of molecular based magnets. Magnetization relaxation experiments also strongly support the occurrence of this quantum phenomenon. This first observation of QTM in a magnetic oxide belonging to the large family of the A3BBO6 compounds opens new opportunities to study a quantum effect in a very different class of materials from molecular magnets.