We present a catalog of 25 definite and 11 probable strong galaxy-galaxy gravitational lens systems with lens redshifts 0.4 lsim z lsim 0.7, discovered spectroscopically by the presence of higher-redshift emission lines within the Baryon Oscillation Spectroscopic Survey (BOSS) of luminous galaxies, and confirmed with high-resolution Hubble Space Telescope (HST) images of 44 candidates. Our survey extends the methodology of the Sloan Lens Advanced Camera for Surveys survey (SLACS) to higher redshift. We describe the details of the BOSS spectroscopic candidate detections, our HST ACS image processing and analysis methods, and our strong gravitational lens modeling procedure. We report BOSS spectroscopic parameters and ACS photometric parameters for all candidates, and mass-distribution parameters for the best-fit singular isothermal ellipsoid models of definite lenses. Our sample to date was selected using only the first six months of BOSS survey-quality spectroscopic data. The full five-year BOSS database should produce a sample of several hundred strong galaxy-galaxy lenses and in combination with SLACS lenses at lower redshift, strongly constrain the redshift evolution of the structure of elliptical, bulge-dominated galaxies as a function of luminosity, stellar mass, and rest-frame color, thereby providing a powerful test for competing theories of galaxy formation and evolution.