This paper introduces a method for finding Bayesian networks for continuous variables in high-dimensional spaces. The paper assumes a Gaussian distribution of any particular random variable when conditioned on its parent nodes. A LASSO objective function is used to construct a sparse set of parent nodes for each random variable, subject to an additional constraint that the resulting structure be an acyclic graph. The network structure constraint is framed as an ordering problem, and an A* search algorithm is proposed which finds a directed acyclic graph which maximizes the LASSO objective function. The LASSO objective function, minus the DAG constraint, is used as an admissible heuristic in the A* search.