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 (Eta Car) during the period 2007 July to 2009 January. We detect a gamma-ray source (1AGL J1043-5931) consistent with the position of Eta Car. If 1AGL J1043-5931 is associated with the Eta 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 pre-periastron period 2007 July to 2008 October is F = (37 +/- 5) x 10-8 ph cm-2 s-1 corresponding to an average gamma-ray luminosity of L = 3.4 x 10^34 erg s-1 for a distance of 2.3 kpc. We also report a 2-day gamma-ray flaring episode of 1AGL J1043-5931 on 2008 Oct. 11-13 possibly related to a transient acceleration and radiation episode of the strongly variable shock in the system.