This presentation reports on first evidence for a low-mass-density/positive-cosmological-constant universe that will expand forever, based on observations of a set of 40 high-redshift supernovae. The experimental strategy, data sets, and analysis techniques are described. More extensive analyses of these results with some additional methods and data are presented in the more recent LBNL report #41801 (Perlmutter et al., 1998; accepted for publication in Ap.J.), astro-ph/9812133 . This Lawrence Berkeley National Laboratory reprint is a reduction of a poster presentation from the Cosmology Display Session #85 on 9 January 1998 at the American Astronomical Society meeting in Washington D.C. It is also available on the World Wide Web at http://supernova.LBL.gov/ This work has also been referenced in the literature by the pre-meeting abstract citation: Perlmutter et al., B.A.A.S., volume 29, page 1351 (1997).