I introduce batman, a Python package for modeling exoplanet transit light curves. The batman package supports calculation of light curves for any radially symmetric stellar limb darkening law, using a new integration algorithm for models that cannot be quickly calculated analytically. The code uses C extension modules to speed up model calculation and is parallelized with OpenMP. For a typical light curve with 100 data points in transit, batman can calculate one million quadratic limb-darkened models in 30 seconds with a single 1.7 GHz Intel Core i5 processor. The same calculation takes seven minutes using the four-parameter nonlinear limb darkening model (computed to 1 ppm accuracy). Maximum truncation error for integrated models is an input parameter that can be set as low as 0.001 ppm, ensuring that the community is prepared for the precise transit light curves we anticipate measuring with upcoming facilities. The batman package is open source and publicly available at https://github.com/lkreidberg/batman .