This paper describes the first homogeneous, flux-limited sample of radio-selected BL Lac objects, taken from the 1 Jy survey of Kuhr et al. These 34 BL Lac objects comprise the only well-defined sample of BL Lac objects outside the X-ray band. The selection criteria include flat radio spectra, optical counterparts visible on Sky Survey Plates, and optical emission lines weaker than 5 angstrom equivalent width in the rest frame. With two exceptions, all of the BL Lac objects also have high optical polarization, P(opt) > 3%. Redshifts from weak emission lines, usually narrow [O II] lambda-3727, [O III] lambda-5007, or broad Mg II lambda-2798, are available for approximately 3/4 of the sample. The nearby (z < 0.2) BL Lac objects, at least, sit in elliptical galaxies and may occur in groups or small clusters of galaxies. Gravitational lensing appears to affect one of the high-redshift (z greater-than-or-similar-to 0.5) BL Lac objects and could be important in others as well. The radio number counts derived from the 1 Jy BL Lac sample are roughly Euclidean over the range between 1 and approximately 5 Jy, and there is evidence for evolution at the 2 sigma-level. The local radio luminosity function of BL Lac objects is derived and the total number density for P5GHz greater-than-or-similar-to 6 x 10(31) ergs s-1 Hz-1 is approximately 40 Gpc-3.