  Context: For over 12 yr, we have carried out a precise radial velocity survey
of a sample of 373 G and K giant stars using the Hamilton \'Echelle
Spectrograph at Lick Observatory. There are, among others, a number of multiple
planetary systems in our sample as well as several planetary candidates in
stellar binaries. Aims: We aim at detecting and characterizing
substellar+stellar companions to the giant star HD 59686 A (HR 2877, HIP
36616). Methods: We obtained high precision radial velocity (RV) measurements
of the star HD 59686 A. By fitting a Keplerian model to the periodic changes in
the RVs, we can assess the nature of companions in the system. In order to
discriminate between RV variations due to non-radial pulsation or stellar spots
we used infrared RVs taken with the CRIRES spectrograph at the Very Large
Telescope. Additionally, to further characterize the system, we obtain
high-resolution images with LMIRCam at the Large Binocular Telescope. Results:
We report the likely discovery of a giant planet with a mass of $m_{p}~\sin
i=6.92_{-0.24}^{+0.18}~M_{Jup}$ orbiting at $a_{p}=1.0860_{-0.0007}^{+0.0006}$
au from the giant star HD 59686 A. Besides the planetary signal, we discover an
eccentric ($e_{B}=0.729_{-0.003}^{+0.004}$) binary companion with a mass of
$m_{B}~\sin i=0.5296_{-0.0008}^{+0.0011}~M_{Sun}$ orbiting at a semi-major axis
of just $a_{B}=13.56_{-0.14}^{+0.18}$ au. Conclusions: The existence of the
planet HD 59686 Ab in a tight eccentric binary system severely challenges
standard giant planet formation theories and requires substantial improvements
to such theories in tight binaries. Otherwise, alternative planet formation
scenarios such as second generation planets or dynamical interactions in an
early phase of the system's lifetime should be seriously considered in order to
better understand the origin of this enigmatic planet.
