Rapid progress in the development of additive manufacturing technologies is opening new opportunities to fabricate structures that control mass transport in three dimensions across a broad range of length scales. We describe a structure that can be fabricated by newly available commercial 3-D printers. It contains an array of regular threedimensional flow paths that are in intimate contact with a solid phase, and thoroughly shuffle material among the paths. We implement a chemically reacting flow model to study its behavior as an exchange chromatography column, and compare it to an array of 1-D flow paths that resemble more traditional honeycomb monoliths. A reaction front moves through the columns and then elutes. The front is sharper at all flow rates for the structure with three-dimensional flow paths, and this structure is more robust to channel width defects than the 1-D array. (C) 2018 American Institute of Chemical Engineers