We present new Chandra observations of the outer halo of the giant elliptical galaxy NGC 4472 (M49) in the Virgo Cluster. The data extend to 130 kpc (28'), and have a combined exposure time of 150 ks. After identifying optical counterparts using the Next Generation Virgo Cluster Survey to remove background active galactic nuclei and globular cluster (GC) sources, and correcting for completeness, we find that the number of field low-mass X-ray binaries (LMXBs) per unit stellar V-band light increases significantly with the galactocentric radius. Because the flux limit of the complete sample corresponds to the Eddington limit for neutron stars in NGC 4472, many of the similar to 90 field LMXBs in this sample could host black holes. The excess of field LMXBs at large galactocentric radii may be partially caused by natal kicks on black holes and neutron stars in binary systems in the inner part of the galaxy. Furthermore, because the metallicity in the halo of NGC 4472 strongly decreases toward larger galactocentric radii, the number of field LMXBs per unit stellar mass is anticorrelated with metallicity, opposite to what is observed in GCs. Another way to explain the spatial distribution of field LMXBs is therefore a reversed metallicity effect, although we have not identified a mechanism to explain this in terms of stellar and binary evolution.