The James Webb Space Telescope (JWST), with its unprecedented sensitivity, will provide a unique set of tools for the study of transiting exoplanets and their atmospheres. The Near Infrared Spectrograph (NIRSpec) is one of four scientific instruments on JWST and offers a high-contrast aperture-spectroscopy mode developed specifically for exoplanet observations. Here we present the NIRSpec Exoplanet Exposure Time Calculator (NEETC) software, an exposure time calculator optimized to evaluate the signal-to-noise ratio and simulate spectra for observations of transiting exoplanets. The NEETC is being developed to help the NIRSpec instrument team, and ultimately future JWST users, to fully investigate NIRSpec's observation modes and the feasibility of exoplanet observations. We give examples of how the NEETC can be used to prepare observations, and present results highlighting the capabilities and limitations of NIRSpec.