  We discuss how a $L_e-L_\mu-L_\tau$ flavour symmetry that is softly broken
leads to keV sterile neutrinos, which are a prime candidate for Warm Dark
Matter. This is to our knowledge the first model where flavour symmetries are
applied simultaneously to active and sterile neutrinos explaining at the same
time active neutrino properties and this peculiar Dark Matter scenario. The
essential point is that different scales of the symmetry breaking and the
symmetry preserving entries in the mass matrix lead to one right-handed
neutrino which is nearly massless compared to the other two. Furthermore, we
naturally predict vanishing $\theta_{13}$ and maximal $\theta_{23}$, while the
correct value of $\theta_{12}$ must come from the mixing of the charged
leptons. We can furthermore predict an exact mass spectrum for the light
neutrinos, which will be testable in the very near future.
