Solar-tracking concentrators can potentially lead to low-cost photovoltaic modules that minimize the use of costly semiconductor materials by improving optical collection and coupling. However, solar concentrators and accompanying trackers have proven to be expensive, bulky, and heavy, thereby resulting in increased balance-of-system costs. Here we demonstrate a lightweight and low-profile, and potentially low-cost planar solar-tracking concentrator based on the ancient Japanese art of origami. The tightly packed hexagonal concentrator and tracker arrays are fabricated by cutting and folding thin reflecting sheets that capture and direct concentrated light onto a small, high-efficiency GaAs solar cell. The tracker enables single-axis solar tracking via a simple one-dimensional translational motion of an actuator with minimal energy expense (∼2.9 J/m2/day). Further, we demonstrate stable operation over 10 000 cycles. The solar concentrated cell achieves a 450% increase in diurnal energy output compared wit...