We measure the cosmological matter density by observing the positions of baryon acoustic oscillations in the clustering of galaxies in the Sloan Digital Sky Survey (SDSS). We jointly analyze the main galaxies and LRGs in the SDSS DR5 sample, using over half a million galaxies in total. The oscillations are detected with 99.74% confidence (3.0 s assuming Gaussianity) compared to a smooth power spectrum. When combined with the observed scale of the peaks within the CMB, we find a best-fit value of sub(M) = 0.256 super(+) sub(-) super(0) sub(0) super(.) sub(.) super(0) sub(0) super(2) sub(2) super(9) sub(4)(68% confidence interval) for a flat cosmology when marginalizing over the Hubble parameter and the baryon density. This value of the matter density is derived from the locations of the baryon oscillations in the galaxy power spectrum and in the CMB, and does not include any information from the overall shape of the power spectra. This is an extremely clean cosmological measurement, as the physics of the baryon acoustic oscillation production is well understood, and the positions of the oscillations are expected to be independent of systematics such as galaxy bias.