  We study (backward) stochastic differential equations with noise coming from
a finite state Markov chain. We show that, for the solutions of these equations
to be `Markovian', in the sense that they are deterministic functions of the
state of the underlying chain, the integrand must be of a specific form. This
allows us to connect these equations to coupled systems of ODEs, and hence to
give fast numerical methods for the evaluation of Markov-Chain BSDEs.
