  Entangling two systems at distant locations using a {\it separable} mediating
ancilla is a counterintuitive phenomenon proposed for qubits by T. Cubitt {\it
et al}. [Phys. Rev. Lett. {\bf 91}, 037902 (2003)]. We show that such
entanglement distribution is possible with Gaussian states, using a certain
three-mode fully separable mixed Gaussian state and linear optics elements
readily available in experiments. Two modes of the state become entangled by
sequentially mixing them on two beam splitters, while the third one remains
separable in all stages of the protocol.
