  We propose a manifestly covariant framework for causal set dynamics. The
framework is based on a structure, dubbed covtree, which is a partial order on
certain sets of finite, unlabeled causal sets. We show that every infinite path
in covtree corresponds to at least one infinite, unlabeled causal set. We show
that transition probabilities for a classical random walk on covtree induce a
classical measure on the $\sigma$-algebra generated by the stem sets.
