  In Euclidean space of dimension 2 or 3, we study a minimum time problem
associated with a system of real-analytic vector fields satisfying
H\"ormander's bracket generating condition, where the target is a nonempty
closed set. We show that, in dimension 2, the minimum time function is locally
Lipschitz continuous while, in dimension 3, it is Lipschitz continuous in the
complement of a set of measure zero. In particular, in both cases, the minimum
time function is a.e. differentiable on the complement of the target. In
dimension 3, in general, there is no hope to have the same regularity result as
in dimension 2. Indeed, examples are known where the minimum time function
fails to be locally Lipschitz continuous.
