Numerous X-ray bursts show strong oscillations in their flux at several hundred hertz as revealed by Rossi X-Ray Timing Explorer. Analyzing one such oscillation from the X-ray binary Aquila X-1, I find that low-energy photons (3.5–5.7 keV) lag high-energy photons (> 5.7 keV) by approximately 1 rad. The oscillations are thought to be produced by hot spots on the spinning neutron star. The lags can then be explained by a Doppler shifting of emission from the hot spots, higher-energy photons being emitted earlier in the spin phase as the spot approaches the observer. A quantitative test of this simple model shows a remarkable agreement with the data. Similar low-energy lags have been measured in kilohertz quasi-periodic oscillations and in the accreting millisecond pulsar SAX J1808. 4-3658. A Doppler delay mechanism may be at work there as well.