We report the first example of a transition to long-range magnetic order in a purely dipolarly interacting molecular magnet. For the magnetic cluster compound Mn6O4Br4(Et2dbm)6, the anisotropy experienced by the total spin S=12 of each cluster is so small that spin-lattice relaxation remains fast down to the lowest temperatures, thus enabling dipolar order to occur within experimental times at Tc=0.16 K. In high magnetic fields, the relaxation rate becomes drastically reduced and the interplay between nuclear- and electron-spin lattice relaxation is revealed.