We report on observations of a solar prominence obtained on 26 April 2007 using the Extreme Ultraviolet Imaging Spectrometer on Hinode. Several regions within the prominence are identified for further analysis. Selected profiles for lines with formation temperatures between log(T)=4.7-6.3, as well as their integrated intensities, are given. The line profiles are discussed. We pay special attention to the He II line which is blended with coronal lines. Our analysis confirms that depression in EUV lines can be interpreted by two mechanisms: absorption of coronal radiation by the hydrogen and neutral helium resonance continua, and emissivity blocking. We present estimates of the He II line integrated intensity in different parts of the prominence according to different scenarios for the relative contribution of absorption and emissivity blocking on the coronal lines blended with the He II line. We estimate the contribution of the He II 256.32 line in the He II raster image to vary between ~44% and 70% of the raster's total intensity in the prominence according to the different models used to take into account the blending coronal lines. The inferred integrated intensities of the He II line are consistent with theoretical intensities obtained with previous 1D non-LTE radiative transfer calculations, yielding a preliminary estimate for the central temperature of 8700 K, central pressure of 0.33 dyn/cm^2, and column mass of 2.5 10^{-4} g/cm^2. The corresponding theoretical hydrogen column density (10^{20} cm^{-2}) is about two orders of magnitude higher than those inferred from the opacity estimates at 195 {Å}. The non-LTE calculations indicate that the He II 256.32 {Å} line is essentially formed in the prominence-to-corona transition region by resonant scattering of the incident radiation. ; Comment: 13 pages, 9 figures and one movie (available at http://www.astro.gla.ac.uk/users/labrosse/movies/sot-26Apr07-3.mpg)