We present a synthetic molecular motor capable of autonomous nanoscale transport in solution. Inspired by bacterial pathogens such as Rickettsia rickettsii, which locomote by inducing the polymerization of the protein actin at their surfaces to form 'comet tails', the motor operates by polymerizing a double-helical DNA tail2. DNA strands are propelled processively at the living end of the growing polymers, demonstrating autonomous locomotion powered by the free energy of DNA hybridization.