  We present what is to our knowledge the first implementation of a
Schr\"odinger cat states "breeding" operation, which allows an iterative growth
of these states. We thus report the experimental generation of a squeezed
Schr\"odinger cat state from two single photon Fock states, which can be seen
as cat states with zero amplitude. These Fock states are mixed on a symmetrical
beamsplitter and the generation is heralded by a homodyne measurement in one of
the two output arms. The output state has a fidelity of 61% with an even
squeezed Schr\"odinger cat state of amplitude $\alpha=1.63$. This hybrid
operation opens up new prospects in quantum optics as the protocol depicted
here can be iterated in order to produce new kind of mesoscopic states.
