A method is presented to collect spatially resolved two-dimensional spectra on a conventional clinical scanner. Time-varying gradients during the readout period rapidly sample data simultaneously for two spatial and two spectral dimensions. The k-space trajectories are based on spiral paths that make efficient use of the gradient hardware. A gridding algorithm is used for reconstruction. With the spiral-based readout gradients, current single-voxel two-dimensional techniques can be extended to spatially resolved volumetric acquisitions. The method is demonstrated with a two-dimensional J-resolved acquisition of a phantom with separate compartments of lactic acid and ethyl alcohol in water. Data were acquired with a spatial resolution of 18 x 18 pixels over a 24 cm field of view, 400 Hz spectral bandwidth in the chemical shift dimension with a 3.8 Hz resolution, and 50 Hz spectral bandwidth in the second frequency dimension with a 1.56 Hz resolution.