We introduce a new technique for imaging the polarized radio sky using interferometric data. The new approach, which we call Faraday synthesis, combines aperture and rotation measure synthesis imaging and deconvolution into a single algorithm. This has several inherent advantages over the traditional two-step technique, including improved sky plane resolution, fidelity, and dynamic range. In addition, the direct visibility- to Faraday-space imaging approach is a more sound foundation on which to build more sophisticated deconvolution or inference algorithms. For testing purposes, we have implemented a basic Faraday synthesis imaging software package including a three-dimensional CLEAN deconvolution algorithm. We compare the results of this new technique to those of the traditional approach using mock data. We find many artifacts in the images made using the traditional approach that are not present in the Faraday synthesis results. In all, we achieve a higher spatial resolution, an improvement in dynamic range of about 20%, and a more accurate reconstruction of low signal to noise source fluxes when using the Faraday synthesis technique.