With the launch date of the James Webb Space Telescope (JWST) growing ever closer, it is imperative that astronomers have access to accurate simulations of JWST observations in order to best plan observations and devise data analysis pipelines. To fill this need, we have developed an open-source time-domain simulator of planetary transits that is capable of creating realistic JWST observations, including noise and systematic errors. Our simulator is based on ExoSim, which produces a time-series collection of images packaged in FITS format, akin to a real observation, derived from a model spectrum. These images include read noise, pointing jitter both above and below the observing cadence, thermal emission by every optical element in the instrument, and intra-pixel quantum-efficiency variations. We have enhanced ExoSim by developing the necessary capabilities to simulate JWST images, such as modeling curved spectral traces, multi-ordered spectra, and JWST detector read-out patterns. We present the development and validation of this tool along with an example simulation of an exoplanet transit. This research was supported by the NASA Exoplanets Research Program grant NNX17AB62G.