We present a catalog of 25 definite and 11 probable strong galaxy-galaxygravitational lens systems with lens redshifts 0.4 <~ z <~ 0.7,discovered spectroscopically by the presence of higher-redshift emissionlines within the Baryon Oscillation Spectroscopic Survey (BOSS) ofluminous galaxies, and confirmed with high-resolution Hubble SpaceTelescope (HST) images of 44 candidates. Our survey extends themethodology of the Sloan Lens Advanced Camera for Surveys survey (SLACS)to higher redshift. We describe the details of the BOSS spectroscopiccandidate detections, our HST ACS image processing and analysis methods,and our strong gravitational lens modeling procedure. We report BOSSspectroscopic parameters and ACS photometric parameters for allcandidates, and mass-distribution parameters for the best-fit singularisothermal ellipsoid models of definite lenses. Our sample to date wasselected using only the first six months of BOSS survey-qualityspectroscopic data. The full five-year BOSS database should produce asample of several hundred strong galaxy-galaxy lenses and in combinationwith SLACS lenses at lower redshift, strongly constrain the redshiftevolution of the structure of elliptical, bulge-dominated galaxies as afunction of luminosity, stellar mass, and rest-frame color, therebyproviding a powerful test for competing theories of galaxy formation andevolution.Based on observations made with the NASA/ESA Hubble Space Telescope,obtained at the Space Telescope Science Institute, which is operated bythe Association of Universities for Research in Astronomy, Inc., underNASA contract NAS 5-26555. These observations are associated withprogram 12209. Based on spectroscopic data from the Baryon OscillationSpectroscopic Survey of the Sloan Digital Sky Survey III.