In this paper, we present ChromoPrint, a method which leverages photochromic dyes to convert resin-based 3D printing - a process that traditionally prints objects from a single material and therefore only a single color - into a multi-color 3D printing process. Rather than using a standard single-color resin, our resin contains a mixture of photochromic dyes that can transition into different colors when exposed to specific wavelengths of light. We modify an existing resin printer to incorporate an RGB projection system which can control each of the photochromic dyes in the resin during printing. By saturating the dyes with a UV light prior to mixing into the resin, and then projecting combinations of RGB light onto each layer after it has been UV cured, we can color objects directly during the printing process. We discuss the formulation of the photochromic resin, the modifications to the printer, the user interface that allows a user to apply color to a 3D model, and the software pipeline that outputs the build instructions to the 3D printer, including the exposure times for curing with UV light and for coloring with the RGB projector.