In this talk, we will consider estimating causal structure from observational data and will assume that the data arise from a linear structural equation model. In this setting, causal structure can be represented as a directed graph, and most previous work has focused on estimating a Markov equivalence class--the set of graphs which can be generically identified by conditional independence tests. Unfortunately, this equivalence class may contain many graphs with conflicting scientific and causal interpretation. However, Shimizu et al (2006) show that an exact graph--not simply an equivalence class--can be identified from observational data if the errors in the structural equation model are non-Gaussian and there is no latent confounding. In this talk we show that the exact causal structure can be recovered in the high dimensional setting given suitable sparsity in the underlying graph. We apply the proposed method to the stocks in the S&P 500 and show that reasonable causal structure is recovered.