  Multi-star systems are common, yet little is known about a stellar
companion's influence on the formation and evolution of planetary systems. For
instance, stellar companions may have facilitated the inward migration of hot
Jupiters towards to their present day positions. Many observed short period gas
giant planets also have orbits that are misaligned with respect to their star's
spin axis, which has also been attributed to the presence of a massive outer
companion on a non-coplanar orbit. We present the results of a multi-band
direct imaging survey using Keck NIRC2 to measure the fraction of short period
gas giant planets found in multi-star systems. Over three years, we completed a
survey of 50 targets ("Friends of Hot Jupiters") with 27 targets showing some
signature of multi-body interaction (misaligned or eccentric orbits) and 23
targets in a control sample (well-aligned and circular orbits). We report the
masses, projected separations, and confirmed common proper motion for the 19
stellar companions found around 17 stars. Correcting for survey incompleteness,
we report companion fractions of $48\%\pm9\%$, $47\%\pm12\%$, and $51\%\pm13\%$
in our total, misaligned/eccentric, and control samples, respectively. This
total stellar companion fraction is $2.8\,\sigma$ larger than the fraction of
field stars with companions approximately $50-2000\,$AU. We observe no
correlation between misaligned/eccentric hot Jupiter systems and the incidence
of stellar companions. Combining this result with our previous radial velocity
survey, we determine that $72\% \pm 16\%$ of hot Jupiters are part of
multi-planet and/or multi-star systems.
