We present the 3D real space clustering power spectrum of a sample of ~600,000 luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS), using photometric redshifts. This sample of galaxies ranges from redshift z=0.2 to 0.6 over 3,528 deg^2 of the sky, probing a volume of 1.5 (Gpc/h)^3, making it the largest volume ever used for galaxy clustering measurements. We measure the angular clustering power spectrum in eight redshift slices and combine these into a high precision 3D real space power spectrum from k=0.005 (h/Mpc) to k=1 (h/Mpc). We detect power on gigaparsec scales, beyond the turnover in the matter power spectrum, on scales significantly larger than those accessible to current spectroscopic redshift surveys. We also find evidence for baryonic oscillations, both in the power spectrum, as well as in fits to the baryon density, at a 2.5 sigma confidence level. The statistical power of these data to constrain cosmology is ~1.7 times better than previous clustering analyses. Varying the matter density and baryon fraction, we find Omega_M = 0.30 pm 0.03, and Omega_b/Omega_M = 0.18 pm 0.04, The detection of baryonic oscillations also allows us to measure the comoving distance to z=0.5; we find a best fit distance of 1.73 pm 0.12 Gpc, corresponding to a 6.5% error on the distance. These results demonstrate the ability to make precise clustering measurements with photometric surveys (abridged).
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