We present results constraining the multiplicity of the very low mass stars and sub-stellar objects in the Orion Nebula Cluster (ONC). Our sample covers primary masses 0.012-0.1M⊙ using archival Hubble Space Telescope data obtained with the Advanced Camera for Surveys using multiple filters. Studying the binary populations of clusters provides valuable constraints of how the birth environment affects binary formation and evolution. Prior surveys have shown that the binary populations of high-mass, high-density star clusters like the ONC may substantially differ from those in low-mass associations. Very low mass stellar and sub-stellar binaries at wide separations, >20AU, are statistically rare in the Galactic field and have been identified in stellar associations like Taurus-Auriga and Ophiuchus. They also may be susceptible to dynamical interactions, and their formation may be suppressed by feedback from on-going star formation. We implement a double point-spread function (PSF) fitting algorithm using empirical, position dependent PSF models to search for binary companions at projected separations > 10 AU (25 mas). With this technique, we identify 7 very low mass binaries, 5 of which are new detections, resulting in a binary frequency of 12+6−3.2% over mass ratios of 0.5 - 1.0 and projected separations of 20 - 200 AU. We find an excess of very low mass binaries in the ONC compared to the Galactic field, with a probability of 10−6 that the populations are statistically consistent. The sub-stellar population of the ONC may require further dynamical processing of the lowest binding energy binaries to resemble the field population.