The Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope detected a gamma-ray source that is spatially consistent with the location of Eta Carinae. This source has been persistently bright since the beginning of the LAT survey observations (from 2008 August to 2009 July, the time interval considered here). The gamma-ray signal is detected significantly throughout the LAT energy band (i.e., up to ~100 GeV). The 0.1-100 GeV energy spectrum is well represented by a combination of a cutoff power-law model (< 10 GeV) and a hard power-law component (> 10 GeV). The total flux (> 100 MeV) is $3.7^{+0.3}_{-0.1} \times 10^{-7}$ photons s$^{-1}$ cm$^{-2}$, with additional systematic uncertainties of 10%, and consistent with the average flux measured by AGILE (Tavani et al. 2009). The light curve obtained by Fermi is consistent with steady emission. Our observations do not confirm the presence of a gamma-ray flare in 2008 October as reported by Tavani et al. (2009), although we cannot exclude that a flare lasting only a few hours escaped detection by the Fermi LAT. We also do not find any evidence for gamma-ray variability that correlates with the large X-ray variability of Eta Carinae observed during 2008 December and 2009 January. We are thus not able to establish an unambiguous identification of the LAT source with Eta Carinae.Read less <