We present the results of extensive observations by the gamma-ray AGILE satellite of the Galactic region hosting the Carina nebula and the remarkable colliding wind binary Eta Carinae (η Car) during the period 2007 July–2009 January. We detect a gamma-ray source (1AGL J1043− 5931) consistent with the position of η Car. If 1AGL J1043− 5931 is associated with the Car system, our data provide the long sought first detection above 100 MeV of a colliding wind binary. The average gamma-ray flux above 100 MeV and integrated over the preperiastron period 2007 July–2008 October is F γ=(37�5)� 10− 8 ph cm− 2 s− 1 corresponding to an average gamma-ray luminosity of L γ= 3.4� 10 34 erg s− 1 for a distance of 2.3 kpc. We also report a two-day gamma-ray flaring episode of 1AGL J1043− 5931 on 2008 October 11–13 possibly related to a transient acceleration and radiation episode of the strongly variable shock in the system.