Context : For over 12 yr , we have carried out a precise radial velocity ( RV ) survey of a sample of 373 G- and K-giant stars using the Hamilton Échelle Spectrograph at the 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 and stellar companions to the giant star HD 59686 A ( HR 2877 , HIP 36616 ) . Methods : We obtained high-precision 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 . To distinguish between RV variations that are due to non-radial pulsation or stellar spots , we used infrared RVs taken with the CRIRES spectrograph at the Very Large Telescope . Additionally , to characterize the system in more detail , we obtained high-resolution images with LMIRCam at the Large Binocular Telescope . Results : We report the probable discovery of a giant planet with a mass of m _ { p } ~ { } \hbox { sin $i$ } = 6.92 _ { -0.24 } ^ { +0.18 } \mathrm { M } _ { \mathrm { Jup } } orbiting at a _ { p } = 1.0860 _ { -0.0007 } ^ { +0.0006 } au from the giant star HD 59686 A . In addition to the planetary signal , we discovered an eccentric ( e _ { B } = 0.729 _ { -0.003 } ^ { +0.004 } ) binary companion with a mass of m _ { B } ~ { } \hbox { sin $i$ } = 0.5296 _ { -0.0008 } ^ { +0.0011 } M _ { \odot } orbiting at a close separation from the giant primary with a semi-major axis of 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 need to be seriously considered to better understand the origin of this enigmatic planet .