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Future space telescopes will directly image extrasolar planets at visiblewavelengths. Time-resolved reflected light from an exoplanet encodesinformation about atmospheric and surface inhomogeneities. Previous researchhas shown that the light curve of an exoplanet can be inverted to obtain alow-resolution map of the planet, as well as constraints on its spinorientation. Estimating the uncertainty on 2D albedo maps has so far remainedelusive. Here we present exocartographer, a flexible open-source Bayesianframework for solving the exo-cartography inverse problem. The map isparameterized with equal-area HEALPix pixels. For a fiducial map resolution of192 pixels, a four-parameter Gaussian process describing the spatial scale ofalbedo variations, and two unknown planetary spin parameters, exocartographerexplores a 198-dimensional parameter space. To test the code, we produce alight curve for a cloudless Earth in a face-on orbit with a 90$^\circ$obliquity. We produce synthetic white light observations of the planet: 5epochs of observations throughout the planet's orbit, each consisting of 24hourly observations with a photometric uncertainty of $1\%$ (120 data). Weretrieve an albedo map and$-$for the first time$-$its uncertainties, along withspin constraints. The albedo map is recognizably of Earth, with typicaluncertainty of $30\%$. The retrieved characteristic length scale is 88$\pm 7^\circ$, or 9800 km. The obliquity is recovered with a $1-\sigma$ uncertaintyof $0.8^\circ$. Despite the uncertainty in the retrieved albedo map, werobustly identify a high albedo region (the Sahara desert) and a largelow-albedo region (the Pacific Ocean).

exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light