Cortico-striato-thalamo-cortical (CSTC) loops are fundamental organizing units in mammalian brains. CSTCs process limbic, associative, and sensorimotor information in largely separated but interacting networks. CTSC loops pass through paired striatal compartments, striosome (aka patch) and matrix, segregated pools of medium spiny projection neurons with distinct embryologic origins, cortical/subcortical structural connectivity, susceptibility to injury, and roles in behaviors and diseases. Similarly, striatal dopamine modulates activity in striosome and matrix in opposite directions. Routing CSTCs through one compartment may be an anatomical basis for regulating discrete functions. We used differential structural connectivity, identified through probabilistic diffusion tractography, to distinguish the striatal compartments (striosome-like and matrix-like voxels) in living humans. We then mapped compartment-specific projections and quantified structural connectivity between each striatal compartment, the globus pallidus interna (GPi), and 20 thalamic nuclei in 221 healthy adults. We found that striosome-originating and matrix-originating streamlines were segregated within the GPi: striosome-like connectivity was significantly more rostral, ventral, and medial. Striato-pallido-thalamic streamline bundles that were seeded from striosome-like and matrix-like voxels transited spatially distinct portions of the white matter. Matrix-like streamlines were 5.7-fold more likely to reach the GPi, replicating animal tract-tracing studies. Striosome-like connectivity dominated in six thalamic nuclei (anteroventral, central lateral, laterodorsal, lateral posterior, mediodorsal-medial, and medial geniculate). Matrix-like connectivity dominated in seven thalamic nuclei (centromedian, parafascicular, pulvinar-anterior, pulvinar-lateral, ventral lateral-anterior, ventral lateral-posterior, ventral posterolateral). Though we mapped all thalamic nuclei independently, functionally-related nuclei were matched for compartment-level bias. We validated these results with prior thalamostriate tract tracing studies in non-human primates and other species; where reliable data was available, all agreed with our measures of structural connectivity. Matrix-like connectivity was lateralized (left > right hemisphere) in 18 thalamic nuclei, independent of handedness, diffusion protocol, sex, or whether the nucleus was striosome-dominated or matrix-dominated. Compartment-specific biases in striato-pallido-thalamic structural connectivity suggest that routing CSTC loops through striosome-like or matrix-like voxels is a fundamental mechanism for organizing and regulating brain networks. Our MRI-based assessments of striato-thalamic connectivity in humans match and extend the results of prior tract tracing studies in animals. Compartment-level characterization may improve localization of human neuropathologies and improve neurosurgical targeting in the GPi and thalamus.