There is a growing interest in the neuroscience community to map the distribution of brain metabolites in vivo. Magnetic resonance spectroscopic imaging (MRSI) is often limited by either a poor spatial resolution and/or a long acquisition time, which severely restricts its applications for clinical and research purposes. Building on a recently developed technique of acquisition-reconstruction for 2D MRSI, we combined a fast Cartesian 1H-FID-MRSI acquisition sequence, compressed-sensing acceleration, and low-rank total-generalized-variation constrained reconstruction to produce 3D high-resolution whole-brain MRSI with a significant acquisition time reduction. We first evaluated the acceleration performance using retrospective undersampling of a fully sampled dataset. Second, a 20 min accelerated MRSI acquisition was performed on three healthy volunteers, resulting in metabolite maps with 5 mm isotropic resolution. The metabolite maps exhibited the detailed neurochemical composition of all brain regions and revealed parts of the underlying brain anatomy. The latter assessment used previous reported knowledge and a atlas-based analysis to show consistency of the concentration contrasts and ratio across all brain regions. These results acquired on a clinical 3 T MRI scanner successfully combined 3D 1H-FID-MRSI with a constrained reconstruction to produce detailed mapping of metabolite concentrations at high resolution over the whole brain, with an acquisition time suitable for clinical or research settings.