We propose and analyze eigenbeam transmission over lineof-sight (LOS) multiple-input multiple-output (MIMO) channels with linear reception. In particular, we consider fixed point-to-point microwave links for which the singular value decomposition of the LOS MIMO channel matrix is analytically derived. We demonstrate that the Tx eigenbeams can be defined without channel state information at the transmitter and that the beams admit an insightful physical interpretation. We also evaluate the performance of a lattice-reduction aided linear receiver through numerical simulations.