The oriented attachment of molecular clusters and nanoparticles in solution is now recognized as an important mechanism of crystal growth in many materials, yet the alignment process and attachment mechanism have not been established. We performed high-resolution transmission electron microscopy using a fluid cell to directly observe oriented attachment of iron oxyhydroxide nanoparticles. The particles undergo continuous rotation and interaction until they find a perfect lattice match. A sudden jump to contact then occurs over less than 1 nanometer, followed by lateral atom-by-atom addition initiated at the contact point. Interface elimination proceeds at a rate consistent with the curvature dependence of the Gibbs free energy. Measured translational and rotational accelerations show that strong, highly direction-specific interactions drive crystal growth via oriented attachment.