We prove that gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. In spite of the obstacle that the objective function is non-convex, we provide polynomial running time and sample complexity bounds under strong but natural assumptions. Linear systems identification has been studied for many decades, yet, to the best of our knowledge, these are the first polynomial guarantees for the problem we consider. Joint work with Tengyu Ma and Benjamin Recht.