The application of Markov chains to modelling refugee crises is explored, focusing on local migration of individuals at the level of cities and days. As an explicit example we apply the Markov chains migration model developed here to UNHCR data on the Burundi refugee crisis. We compare our method to a state-of-the-art `agent-based' model of Burundi refugee movements, and highlight that Markov chain approaches presented here can improve the match to data while simultaneously being more algorithmically efficient.