While radio-based indoor localization schemes achieve decimeter-scale accuracy, they typically require precise reference measurements or multiple infrastructure nodes with redundant localization anchors. In this paper, we propose Pseudo LATeration (PLAT), an indoor localization protocol that requires only a single infrastructure anchor and does not require prior knowledge of the environment. PLAT leverages the directionality and propagation characteristics of millimeter-wave transmissions to relax the requirement of multiple infrastructure anchors and constructs virtual anchors for multilateration from reflected signal paths. By combining these virtual anchors with time-of-flight measurements for distance estimation, PLAT can localize user devices in indoor environments with only a single infrastructure node. Our evaluation reveals centimeter scale location accuracy for typical office environments. In testbed measurements and simulations, localization errors are below 10 cm for distances up to 1.5 m and beamwidths below 10 degrees. Although accuracy decreases with distance, we show that multiple reflection paths can mitigate this effect.