  This paper is concerned with Chern-Ricci flow evolution of left-invariant
hermitian structures on Lie groups. We study the behavior of a solution, as t
is approaching the first time singularity, by rescaling in order to prevent
collapsing and obtain convergence in the pointed (or Cheeger-Gromov) sense to a
Chern-Ricci soliton. We give some results on the Chern-Ricci form and the Lie
group structure of the pointed limit in terms of the starting hermitian metric
and, as an application, we obtain a complete picture for the class of solvable
Lie groups having a codimension one normal abelian subgroup. We have also found
a Chern-Ricci soliton hermitian metric on most of the complex surfaces which
are solvmanifolds, including an unexpected shrinking soliton example.
