In this paper, we investigate the optimization of non-uniform linear antenna arrays (NULAs) for millimeter wave (mmWave) line-of-sight (LoS) multiple-input multiple-output (MIMO) channels. Our focus is on the maximization of the system effective multiplexing gain (EMG), by optimizing the individual antenna positions in the transmit/receive NULAs. Here the EMG is defined as the number of signal streams that are practically supported by the channel at a finite SNR. We first derive analytical expressions for the asymptotic channel eigenvalues with arbitrarily deployed NULAs when, asymptotically, the end-to-end distance is sufficiently large compared to the aperture sizes of the transmit/receive NULAs. Based on the derived expressions, we prove that, the asymptotically optimal NULA deployment that maximizes the achievable EMG should follow the groupwise Fekete-point distribution. Specifically, the antennas should be physically grouped into K separate uniform linear antenna arrays (ULAs) with the minimum feasible antenna spacing within each ULA, where K is the target EMG to be achieved; in addition, the centers of these K ULAs follow the Fekete-point distribution. We numerically verify the asymptotic optimality of such an NULA deployment and extend it to a groupwise projected arch type (PAT) NULA deployment, which provides a more practical option for mmWave LoS MIMO systems with realistic non-asymptotic configurations. Numerical examples are provided to demonstrate a significant capacity gain of the optimized NULAs over traditional ULAs.