A Riemannian manifold is said to have higher (Euclidean) rank if, along every geodesic, there is at least one parallel Jacobi field other than its velocity vector. A classical result due to Ballmann, and independently Burns and Spatzier, states that finite-volume manifolds with nonpositive sectional curvature and higher rank are either locally symmetric or have reducible universal covering. This rank rigidity statement has been generalized by relaxing the finite-volume assumption (Eberlein and Heber), and replacing nonpositive sectional curvature by the absence of focal points (Watkins). In this talk, I will show that rank rigidity holds in dimension 3 without any further assumptions: a complete 3- manifold has higher rank if and only if its universal covering splits isometrically as a product. This is joint work with Ben Schmidt (MSU).