Electromagnetically induced transparency is a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium; a 'coupling' laser is used to create the interference necessary to allow the transmission of resonant pulses from a 'probe' laser. This technique has been used to slow and spatially compress light pulses by seven orders of magnitude, resulting in their complete localization and containment within an atomic cloud. Here we use electromagnetically induced transparency to bring laser pulses to a complete stop in a magnetically trapped, cold cloud of sodium atoms. Within the spatially localized pulse region, the atoms are in a superposition state determined by the amplitudes and phases of the coupling and probe laser fields. Upon sudden turn-off of the coupling laser, the compressed probe pulse is effectively stopped; coherent information initially contained in the laser fields is 'frozen' in the atomic medium for up to 1 ms. The coupling laser is turned back on at a later time and the probe pulse is regenerated: the stored coherence is read out and transferred back into the radiation field. We present a theoretical model that reveals that the system is self-adjusting to minimize dissipative loss during the 'read' and 'write' operations. We anticipate applications of this phenomenon for quantum information processing.