Dark matter consisting of Weakly-interacting Massive Particles (WIMPs) makes up most of the matter in the universe. WIMPs have not yet been convincingly detected in the laboratory, despite several intriguing hints. Direct-detection experiments exploit the fact that a nucleus struck by a WIMP will recoil elastically, depositing its energy in the surrounding medium. However they are unable to measure the recoil direction. Directional capability would allow observation of distinctive features WIMP interactions that would not be expected from terrestrial backgrounds--e.g. the diurnal modulation caused by the earth's rotation. We propose to develop a radically different detector concept based on ordered arrays of single-stranded DNA. A nucleus that recoils through such an array would sever the strands it encounters. The fragments would be collected, amplified, and sequenced, allowing the reconstruction of the track with nanometer-level precision. Applications of such a precision tracker to problems beyond WIMP detection are also enticing.