  Using the known detection limits for high-resolution imaging observations and
the statistical properties of true binary and line-of-sight companions, we
estimate the binary fraction of {\it Kepler} exoplanet host stars. Our speckle
imaging programs at the WIYN 3.5-m and Gemini North 8.1-m telescopes have
observed over 600 {\it Kepler} objects of interest (KOIs) and detected 49
stellar companions within $\sim$1 arcsecond. Assuming binary stars follow a
log-normal period distribution for an effective temperature range of 3,000 to
10,000 K, then the model predicts that the vast majority of detected
sub-arcsecond companions are long period ($P>50$ years), gravitationally bound
companions. In comparing the model predictions to the number of real detections
in both observational programs, we conclude that the overall binary fraction of
host stars is similar to the 40-50\% rate observed for field stars.
