  This article discusses the concept of rational equivalence in tropical
geometry (and replaces the older and imperfect version arXiv:0811.2860). We
give the basic definitions in the context of tropical varieties without
boundary points and prove some basic properties. We then compute the "bounded"
Chow groups of $\mathbb{R}^n$ by showing that they are isomorphic to the group
of fan cycles. The main step in the proof is of independent interest: We show
that every tropical cycle in $\mathbb{R}^n$ is a sum of (translated) fan
cycles. This also proves that the intersection ring of tropical cycles is
generated in codimension 1 (by hypersurfaces).
