We present results from an archival study of 70 medium-redshift QSOs observed with the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. The QSOs have magnitudes M_V < -23 (total nuclear plus host light) and redshifts 0.06 < z < 0.46. A close relationship between QSO host and nucleus is found by examining multiple parameters at once. A principal components analysis shows that 3 nuclear and host properties are related in a kind of fundamental plane: nuclear luminosity and the size and effective surface magnitude of the bulge. Using optical nuclear luminosity, this relationship explains 95.9% of the variance in the overall sample, while 94.9% of the variance is accounted for if we use x-ray nuclear luminosity. The form of this QSO fundamental plane shows similarities to the well-studied fundamental plane of elliptical galaxies, and we examine the possible relationship between them as well as the difficulties involved in establishing this connection. The key to the relationship might lie in the fueling mechanism of the central black hole. Comment: 6 pages, 2 figures, TeX uses elsart.cls, from workshop "QSO Host Galaxies: Evolution and Environment" (Univ. Leiden, Aug. 22-26, 2005)