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Sorting cells by their type is an important capability in biological research and medical diagnostics. However, most cell sorting techniques rely on labels or tags, which may have limited availability and specificity. Sorting different cell types by their different physical properties is an attractive alternative to labels because all cells intrinsically have these physical properties. But some physical properties, like cell size, vary significantly from cell to cell within a cell type; this makes it difficult to identify and sort cells based on their sizes alone. In this work we continuously sort different cells types by their density, a physical property with much lower cell-to-cell variation within a cell type (and therefore greater potential to discriminate different cell types) than other physical properties. We accomplish this using a 3D-printed microfluidic chip containing a horizontal flowing micron-scale density gradient. As cells flow through the chip, Earth's gravity makes each cell move vertically to the point where the cell's density matches the surrounding fluid's density. When the horizontal channel then splits, cells with different densities are routed to different outlets. As a proof of concept, we use our density sorter chip to sort polymer microbeads by their material (polyethylene and polystyrene) and blood cells by their type (white blood cells and red blood cells). The chip enriches the fraction of white blood cells in a blood sample from 0.1% (in whole blood) to nearly 98% (in the output of the chip), a 1000x enrichment. Any researcher with access to a 3D printer can easily replicate our density sorter chip and use it in their own research using the design files provided as online Supporting Information. Additionally, researchers can simulate the performance of a density sorter chip in their own applications using the Python-based simulation software that accompanies this work. The simplicity, resolution, and throughput of this technique make it suitable for isolating even rare cell types in complex biological samples, in a wide variety of different research and clinical applications.