In this paper, we investigate the optimal line-of-sight (LoS) coverage problem for multiple access point (multi-AP) mmWave wireless LANs in indoor scenarios. Due to the weak diffraction ability of mmWave signals at 60 GHz, maintaining LoS communications between APs and client devices is critical to achieve ultra-high data rates with mmWave communications. We focus on the use of multiple APs deployed to maximize LoS coverage in a target area, and we develop multi-AP placements that maximize LoS coverage by means of both analytical and algorithmic methods. We consider two main scenarios, which differ in their assumptions about knowledge of obstacles and clients. In a random-obstacle, random-client scenario, we derive the LoS-optimal positions of APs by solving a thinnest covering problem. For a fixed-obstacle, random-client scenario, we propose an efficient algorithm that produces a multi-AP placement, which is shown through simulation to provide near-optimal LoS coverage. Finally, through extensive ns-3 simulations based on the IEEE 802.11ad protocol and mmWave-specific channel models, we show that our multi-AP placements are significantly better than existing placement approaches, both in terms of LoS coverage and aggregate throughput.