Dispersion interferometers have been used to measure line integrated electron densities from many fusion devices. To optically suppress noise due to mechanical vibrations, a conventional dispersion interferometer typically uses two nonlinear crystals located before and after the plasma along the laser beam path. Due to the long beam path, it can be difficult to overlap the fundamental and second harmonic laser beams for a heterodyne dispersion interferometer and to focus the beams on the second nonlinear crystal located after the plasma, especially when the aperture of the nonlinear crystal is small, i.e., of the order of mm. To overcome such difficulties, a new concept of a heterodyne dispersion interferometer, a single crystal dispersion interferometer (SCDI), is developed and installed on KSTAR with the laser wavelength of 1064 nm. The concept and the optical setup of the KSTAR SCDI are discussed, as well as its first measurement during a shattered pellet injection that produces abrupt and large changes in the electron density. To demonstrate feasibility, the KSTAR SCDI measurements are also compared with those from the existing two-color interferometer.