Traditional differential astrometric techniques are limited in precision by the atmosphere in a way that does not show much improvement with increased telescope aperture. However, greatly improved astrometric precision may be obtainable by exploiting the strong aperture dependence of the spatial correlation between simultaneously recorded specklegrams within the speckle isoplanatic angle. The cross-correlation of two speckle images of a binary star pair may yield higher astrometric precision in the measurement of the binary separation than centroid differences. The degree of this improvement, however, depends strongly upon the effective thickness of the turbulence in the atmosphere. A 5- minute observation using a large-format, rapid-readout CCD at a 2.3-m telescope has demonstrated 1-milliarcsec precision in the determination of the separation of a 7.3 arcsec binary star pair when processed with speckle techniques.