How do people think about time? Here we describe representations of time in Pormpuraaw, a remote Australian Aboriginal community. Pormpuraawans' representations of time differ strikingly from all others documented to date. Previously, people have been shown to represent time spatially from left to right or right to left, or from front to back or back to front. All of these representations are with respect to the body. Pormpuraawans instead arrange time according to cardinal directions: east to west. That is, time flows from left to right when one is facing south, from right to left when one is facing north, toward the body when one is facing east, and away from the body when one is facing west. These findings reveal a qualitatively different set of representations of time, with time organized in a coordinate frame that is independent from others reported previously. The results demonstrate that conceptions of even such fundamental domains as time can differ dramatically across cultures.