We propose a methodology for predicting the printability of an alloy, subject to laser powder bed fusion additive manufacturing. Regions in the process space associated with keyhole formation, balling, and lack of fusion are assumed to be strong functions of the geometry of the melt pool, which in turn is calculated for various combinations of laser power and scan speed via a Finite Element thermal model that incorporates a novel vaporization-based transition from surface to volumetric heating upon keyhole formation. Process maps established from the Finite Element simulations agree with experiments for a Ni-5wt.%Nb alloy and an equiatomic CoCrFeMnNi High Entropy Alloy and suggest a strong effect of chemistry on alloy printability. The printability maps resulting from the use of the simpler Eagar-Tsai model, on the other hand, are found to be in disagreement with experiments due to the oversimplification of this approach. Uncertainties in the printability maps were quantified via Monte Carlo sampling of a multivariate Gaussian Processes surrogate model trained on simulation outputs. The printability maps generated with the proposed method can be used in the selection—and potentially the design—of alloys best suited for Additive Manufacturing.