Swept-carrier time-domain optical memory [Opt. Lett. 17, 535 (1992)] has been proposed as a means of storing optical data streams in inhomogeneously broadened spectral recording materials. The process provides for full utilization of the material storage bandwidth regardless of the data rate and permits storage of data sequences with durations exceeding the material dephasing time. We report what we believe is the first experimental demonstration of this storage process. Our experiments, implemented with frequency-swept diode lasers and Tm3+:YAG storage material, demonstrate single-event storage of 98-bit data streams whose duration is an order of magnitude longer than the material dephasing time.