(eng): This paper introduces a new underwater acoustic eigenstructure ESPRIT-based algorithm that yields closed-form direction-of arrival (DOA) estimates using a single vector-hydrophone. A vector-hydrophone is composed of two or three spatially co-located but orthogonally oriented velocity-hydrophones plus another optional co-located pressure hydrophone. This direction finding algorithm may resolve up to four monochromatic sources. Cramer-Rao bounds for arrival angle estimates for this scenario are also derived.