THE MASSIVE STELLAR BINARY SYSTEM ETA CARINAE DRIVES STRONG SHOCKS BY THE COLLISION OF WINDS FROM TWO STARS. OUR NUSTAR OBSERVATIONS OF ETA CARINAE IN 2015 AND 2016 DETECTED AN EXTREMELY HARD X-RAY COMPONENT OVER THE THERMAL EMISSION ABOVE 15 KEV. THE APPARENT ABSENCE OF THIS COMPONENT DURING THE 2-10 KEV X-RAY MINIMUM AROUND PERIASTRON INDICATES THAT THE SOURCE IS LOCATED VERY CLOSE TO THE WIND COLLIDING REGION. THIS COMPONENT MAY ORIGINATE FROM INVERSE-COMPTON SCATTERING OF STELLAR UV BY ACCELERATED NON-THERMAL PARTICLES AND MAY BE RELATED TO THE FERMI GEV GAMMA-RAY SOURCE. WE PROPOSE A NUSTAR OBSERVATION OF THE STAR IN AO3 TO MONITOR ITS VARIATION WHEN THE GAMMA-RAY EMISSION ABOVE 10 GEV IS EXPECTED TO INCREASE AND THUS ESTABLISH A CRUCIAL CORRELATION BETWEEN THE TWO RANGES.