This paper describes an approach to obtain three-dimensional (3D) imaging measurements in turbulent flames at kHz rate based on tomographic chemiluminescence (TC). Such measurement capability has been long desired to resolve the inherent 3D spatial structures and temporal dynamics of turbulent flames. In this work, five high-speed cameras were employed to simultaneously record projection measurements of chemiluminescence emissions of turbulent jet flames from five different view angles 1 and 2 kHz. These projection measurements were then used as the inputs for a tomography inversion algorithm to yield the 3D instantaneous spatial structures of the flames in a measurement region of ~16×16×16 cm. To our knowledge, this paper represents the first demonstration of instantaneous 3D combustion imaging across a sizable measurement volume at kHz.