Using Hubble Space Telescope observations of the globular cluster NGC 6397, we constrain the cluster's binary fraction. The observations consist of two fields: the primary science field, a single Advanced Camera for Surveys (ACS) pointing centered approximately 5' from the cluster center; and the parallel field, a single WFPC2 field centered on the cluster center. Using the exquisite photometric precision of these observations, we determine the binary fraction in these regions of the cluster by examining stars lying off the main sequence. The binary fraction is constrained to be 0.012 ± 0.004 in the ACS field, and to be 0.051 ± 0.010 in the WFPC field. N-body simulations by Hurley et al. in 2007 suggest that the binary fraction remains nearly constant beyond the half-mass radius for the lifetime of the cluster. In the context of these simulations, our results suggest that NGC 6397 had a primordial binary fraction of only ~1%.Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. These observations are associated with proposals GO-10424.