I will report on an ongoing joint project with M. Shapiro and A. Vainshtein devoted to a conjectural correspondence between classes in the Belavin-Drinfeld classification of of Poisson-Lie structures on a simple Lie groups and cluster algebra structures in the ring of regular functions on the group. I will concentrate on the case associated with the Cremmer-Gervais r-matrix - the farthest away from the standard Poisson-Lie structure on SL(n) - and describe the corresponding cluster algebra.