Astrophys.J. 598 (2003) 481-485 We report the discovery of millisecond oscillations in an X-ray burst from the X-ray transient SAX J1748.9-2021 in the globular cluster NGC 6440. Oscillations at a frequency of 409.7 +/- 0.3 Hz were present in one of nine X-ray bursts observed with the Proportional Counter Array on the Rossi X-ray Timing Explorer during the outburst which occurred in 2001. The burst was one of the two dimmest and had the longest duration and decay time. The average peak luminosity of two bursts showing radius expansion is (3.6 +/- 0.4) x 10^38 erg/s, consistent with the Eddington luminosity for a 1.4 solar mass and 10 km radius neutron star burning hydrogen-poor matter. We speculate that the dichotomy observed between sources with burst oscillations at once versus twice the frequency difference of kHz quasiperiodic oscillations in the persistent emission may be related to the magnetic field geometry of the neutron stars.