Three-dimensional (3D) imaging sensors enable machines to perceive, map, and interact with the surrounding world. The size of light detection and ranging (LiDAR) devices is often limited by mechanical scanners. Focal plane array-based 3D sensors are promising candidates for solid-state LiDARs because they enable electronic scanning without mechanical moving parts, however, their resolutions have been limited to 512 pixels or smaller. In this paper, we report on a 16,384-pixel LiDAR with a wide field of view (70°×70°), a fine addressing resolution (0.6°×0.6°), a narrow beam divergence (0.050°×0.049°), and a random-access beam addressing with sub-MHz operation speed. The 128×128-element focal plane switch array (FPSA) of grating antennas and micro-electro-mechanical system (MEMS)-actuated optical switches are monolithically integrated on a 10×11 mm2 silicon photonic chip, where a 128×96 sub-array is wire-bonded and tested in experiments. 3D imaging with a distance resolution of 1.7 cm is achieved with frequency-modulated continuous-wave (FMCW) ranging in monostatic configuration. The FPSA can be mass-produced in complementary metal-oxide-semiconductor (CMOS) foundries, which will enable ubiquitous 3D sensors for autonomous cars, drones, robots, and smartphones.