Low resolution spectra have been obtained of eight R almost-equal-to 19 mag galaxies located within 1 arcmin of the low-redshift, high luminosity quasar H1821 + 643. Six of the eight galaxies belong to a cluster that has the same redshift, within the observational errors, as the quasar. Five of the six cluster members have the spectra of early type galaxies; the spectrum of the sixth cluster member contains H-alpha, O III], and possibly O II emission lines. The other two objects are an emission line foreground galaxy and a background galaxy. The cluster has a Galactocentric redshift of 0.299 +/- 0.002 and a radial velocity dispersion of 1050 +/- 320 km s-1. The photometric and spectroscopic data suggest that H1821 + 643 is associated with a rich cluster of galaxies.