We present 8.4 GHz very long baseline interferometry (VLBI) observations of 69 southern hemisphere extragalactic sources in the International Celestial Reference Frame. These are the first in a series of observations intended to image all such sources at milliarcsecond resolution in order to determine their continued suitability for reference-frame use based on intrinsic structure. We use the resultant images to calculate a core fraction, that is, the ratio of core flux density to total flux density, for all observed sources. The resulting distribution, with a mean value of 0.83, suggests that most sources are relatively compact. However, just over half the observed sources show significant extended emission in the form of multiple compact components. These sources are probably poorly suited for high-accuracy reference-frame use unless intrinsic structure and potential variability can be taken into account. Our observations represent the first large, comprehensive VLBI imaging survey in the southern hemisphere, significantly extending the existing limited VLBI surveys and, along with some well-known objects, containing many sources that have never been imaged at milliarcsecond resolution. The overlap with Very Long Baseline Array images of sources between 0° and -35° declination helps determine the limits to imaging with the southern hemisphere–accessible telescopes.