  The steady state for a system of N particle under the influence of an
external field and a Gaussian thermostat and colliding with random "virtual"
scatterers can be obtained explicitly in the limit of small field. We show the
sequence of steady state distribution, as N varies, forms a chaotic sequence in
the sense that the k particle marginal, in the limit of large N, is the k-fold
tensor product of the 1 particle marginal. We also show that the chaoticity
properties holds in the stronger form of entropic chaoticity.
