The technique of Burst Mode (BM) VLBI is described and its particular application to the observations of pulsars is explored. The wideband pulsed radiation from these objects is exploited to acquire data at two ends of an interferometer baseline in high-speed bursts and only during the pulsar on-times. The result at the VLBI correlator is an improvement in sensitivity by as much as the inverse pulsar duty cycle, and is a consequence of the bandwidth expansion offered by BM and the intrinsic use of gating. As a result, precision astrometrical studies of pulsars will benefit through the greatly increased instantaneous bandwidths achieved by pulsar BM. The problems, implications, and limitations of acquiring and processing pulsar BM data are discussed.