We have found broad H alpha and H beta line emission in spectra of BL Lacertae taken on 1995 May 21 and June 1: on those occasions BL Lac did not meet the defining criteria for the class named after it. The H alpha line luminosity, ~2 x 1041 h-2 erg s-1 for H0 = 100 h km s-1 Mpc-1, is significantly above the detection threshold in older published spectra which do not show the line. Several possible explanations for the increase in broad line luminosity are discussed. The continuum was at the faint end of its commonly observed range: V ~ 16.0 on 1995 May 21. The polarization, measured on 1995 June 1, was also near the low end of the typical range in BL Lac: ~5.0% in PA ~ 22 deg near 7500 A, rising to ~6.1% in PA ~ 15 deg near 4900 A. Absorption features in the spectrum show the presence of the associated galaxy, but the light is still dominated by an underlying smooth continuum, the intrinsic shape of which is well approximated between 8000 and 4000 A by F nu ~ nu -1.7, indicating a synchrotron origin. We confirm the narrow emission line redshift, z = 0.0686 +/- 0.0004.