During the Astro-1 mission in 1990 December, the Hopkins Ultraviolet Telescope (HUT) was used to observe the extreme ultraviolet spectrum (415-912 angstrom) of the hot DA white dwarf G191-B2B. Absorption by neutral helium shortward of the 504 angstrom He I absorption edge is clearly detected in the raw spectrum. Model fits to the observed spectrum require interstellar neutral helium and neutral hydrogen column densities of 1.45 +/- 0.065 x 10(17) cm-2 and 1.69 +/- 0.12 x 10(18) cm-2, respectively. Comparison of the neutral columns yields a direct assessment of the ionization state of the local interstellar cloud surrounding the Sun. The neutral hydrogen to helium ratio of 11.6 +/- 1.0 observed by HUT, like the lower signal-to-noise results of a similar measurement by Green, Jelinsky, & Bowyer (1990b), strongly contradicts the widespread view that hydrogen is much more ionized than helium in the local interstellar medium, a view which has motivated some exotic theoretical explanations for the supposed high ionization. In fact, the HUT observation implies somewhat greater ionization of helium than hydrogen in the local cloud, consistent with models of the local cloud based on known sources of ionization. Consistency with solar radiation backscatter measurements can be achieved if a neutral hydrogen attenuation mechanism such as the charge-exchange proposed by Ripken & Fahr (1983) operates at the heliopause. In that case, adjusting the typical backscatter-derived local densities for such an effect. we find that within the local cloud the particle densities are n(H) congruent-to 0.13-0.15 cm-3, n(He) congruent-to 0.01 3-0.015 cm-3 and n(e) congruent-to 0.03 cm-3; the ionized fractions are X(H) congruent-to 0.1-0.2 and X(He) congruent-to 0.1-0.35; the total hydrogen column density of the local cloud toward G191-B2B is approximately 2.2 x 10(18) CM-2 ; and the cloud extends approximately 5 pc in that direction.