  We describe those complete linearly ordered topological spaces $X$ which are
homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open
interval in $X$. Using countable tail-like ordinals as indices, we build towers
of distinct CHLOTS. Using tree constructions we are able to extend the towers
and to describe an inductive procedure which yields every CHLOTS.
