An elongated dipolar gas can undergo a structural instability from a linear to a zigzag configuration when the interaction energy overcomes the confining potential. Naively this entails breaking of Z₂ symmetry. However, quantum fluctuations in the particle positions along the condensate can continuously deform the zigzag structure thus restoring the Z₂ symmetry. By taking the proper continuum limit, we show that the Zigzag nevertheless survives as a well defined topological phase, characterized by a non local order parameter.