We  consider   distributions  of  ordered  random   vectors  with  given
one-dimensional marginal distributions. We  give an elementary necessary
and sufficient condition  for the existence of such  a distribution with
finite entropy.  In this  case, we  give explicitly  the density  of the
unique distribution which  achieves the maximal entropy  and compute the
value of its entropy. This density is the unique one which has a product
form on its  support and the given one-dimensional  marginals. The proof
relies  on the  study  of copulas  with  given one-dimensional  marginal
distributions for its order statistics.