Fast, 3D imaging of living cells is a vital tool for studying complex biological processes. However, current fluorescence and phase imaging techniques either achieve maximum volumetric frame rates of less than 1 kHz or do not provide true 3D information in complex environments. While this is sufficient in many biological contexts, it is not fast enough to reveal e.g. the motion of cilia which beat at 100 Hz during swimming of some protists. Achieving kilohertz rate, true 3D volumetric imaging is an unmet challenge which would shed new light on this and other previously inaccessible regimes. To meet this challenge, we develop an optical diffraction tomography (ODT) instrument which utilizes a novel pattern generation scheme to overcome existing limitations to multiplexing, and achieves kilohertz volumetric frame rate 3D imaging. This approach adapts ODT, which has most often been considered in a biomedical context, to the unique requirements of biophysics and soft matter experiments. We construct ODT patterns using a technique we refer to as Fourier pattern synthesis which enables high-quality pattern projection using binary digital micromirror device patterns and multiplexing tens to hundreds of views. We utilize this approach to multiplex ∼150 ODT views in as few as 8 images and study how reconstruction quality changes with multiplexing. We demonstrate our approach on a variety of samples, including cells and diffusing colloidal particles.