We study the problem of sparse recovery in an overcomplete dictionary. This problem has attracted considerable attention in signal processing, statistics, and computer science, and a variety of algorithms have been developed to recover the sparse vector. We propose a new method based on the computationally efficient Viterbi algorithm which is shown to achieve better performance than competing algorithms such as Orthogonal Matching Pursuit (OMP), Orthogonal Least-Squares (OLS), Multi-Branch Matching Pursuit (MBMP), Iterative Hard Thresholding (IHT), and l1 minimization. We also explore the relationship of the Viterbi-based approach with OLS.