As we approach the James Webb Space Telescope (JWST) era, several studies have emerged that aim to (1) characterize how the instruments will perform and (2) determine what atmospheric spectral features could theoretically be detected using transmission and emission spectroscopy. To some degree, all these studies have relied on modeling of JWST's theoretical instrument noise. With under two years left until launch, it is imperative that the exoplanet community begins to digest and integrate these studies into their observing plans, as well as think about how to leverage the Hubble Space Telescope (HST) to optimize JWST observations. To encourage this and to allow all members of the community access to JWST & HST noise simulations, we present here an open-source Python package and online interface for creating observation simulations of all observatory-supported timeseries spectroscopy modes. This noise simulator, called PandExo, relies on some aspects of Space Telescope Science Institute's Exposure Time Calculator, Pandeia. We describe PandExo and the formalism for computing noise sources for JWST. Then we benchmark PandExo's performance against each instrument team's independently written noise simulator for JWST, and previous observations for HST. We find that PandExo is within 10% agreement for HST/WFC3 and for all JWST instruments.