  Chow varieties are a parameter space for cycles of a given variety of a given
codimension and degree. We construct their analog for differential algebraic
varieties with differential algebraic subvarieties, answering a question of
Gao, Li and Wei. The proof uses the construction of classical algebro-geometric
Chow varieties, the theory of characteristic sets of differential varieties,
the theory of prolongation spaces, and the theory of differential Chow forms.
In the course of the proof several definability results from the theory of
algebraically closed fields are required. Elementary proofs of these results
are given in an appendix by William Johnson.
