  A point contact in a Luttinger liquid couples the left- and right-moving
channels, producing shot noise. We calculate exactly the DC shot noise at zero
temperature in the out-of-equilibrium steady state where current is flowing.
Integrability of the interaction ensures the existence of a quasiparticle basis
where quasiparticles scatter ``one by one'' off the point contact. This enables
us to apply a direct generalization of the Landauer approach to shot noise to
this interacting model. We find a simple relation of the noise to the current
and the differential conductance. Our results should be experimentally-testable
in a fractional quantum Hall effect device, providing a clear signal of the
fractional charge of the Laughlin quasiparticles.
