  In this work we present a simple and efficient algorithm which, with high
probability, provides an almost uniform sample from the set of proper
k-colourings on an instance of a sparse random graph G(n,d/n), where k=k(d) is
a sufficiently large constant. Our algorithm is not based on the Markov Chain
Monte Carlo method (M.C.M.C.). Instead, we provide a novel proof of correctness
of our Algorithm that is based on interesting "spatial mixing" properties of
colourings of G(n,d/n). Our result improves upon previous results (based on
M.C.M.C.) that required a number of colours growing unboundedly with n.
