We propose an automatic preconditioning scheme for large sparse numerical optimization. The strategy is based on an examination of the sparsity pattern of the Hessian matrix: using a graph-theoretic heuristic, a block diagonal approximation to the Hessian matrix is induced. The blocks are submatrices of the Hessian matrix; furthermore, each block is chordal. That is, under a positive definiteness assumption, each block can be Cholesky factored without creating new nonzeroes (fill). Therefore the preconditioner is space efficient. We conduct a number of numerical experiments to determine the effectiveness of the preconditioner in the context of a linear conjugate gradient algorithm for optimization.