An optical buffer having a large delay-bandwidth-product -- a critical component for future all-optical communications networks -- remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity in free space is continuously tunable provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of ~100 for pulses of width ~1 ps are observed, with no fundamental limit on the system bandwidth.
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