We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t(*)>or=t(r). We conclude that the cold atom ratchets require Db/ variant Planck's over 2pi approximately 1, where b is a small deviation from period-one pulses.