"VLBI astrometry provides extremely accurate positional information for compact radio sources,such as pulsars, masers and AGN. Building a series of position measurements over time allows the measurement of the distance and kinematics of a source, which can be used to reveal information about the source or its environment. However, VLBI astrometry is very demanding technically, requiring relative delay measurements on the order of picoseconds. Attaining these accuracies requires very good control over sources of systematic error in the VLBI array. In this talk, I will describe the major sources of delay error which must be controlled in an astrometric experiment, and how this was achieved for the Long Baseline Array, a VLBI array in Australia which had not previously been used for precision astrometry. The added difficulties encountered for Southern Hemisphere astrometry will be discussed, and the results obtained will be contrasted to those obtained with Northern Hemisphere instruments such as the VLBA."