We present some results from our HST archival image study of 71 QSO host galaxies. The objects are selected to have z < 0.46 and total absolute magnitude M_V < -23 (H_0=50 km/s/Mpc). This initial study investigates host morphology and radio loudness, and it derives the QSO host galaxy luminosity function. We have analyzed available WFPC2 broad band images, using a uniform set of procedures. The host galaxies span a narrow range of luminosities and are exceptionally bright, much more so than normal galaxies, usually L > L*_V. The QSOs are almost equally divided among radio-loud QSOs with elliptical hosts, radio-quiet QSOs with elliptical hosts, and radio-quiet QSOs with spiral hosts. Using a weighting procedure, we derive the combined luminosity function of QSO host galaxies. We find that the luminosity function of QSO hosts differs in shape from that of normal galaxies but that they coincide at the highest luminosities. The ratio of the number of quasar hosts to the number of normal galaxies at a luminosity L_V is R = [L_V/(11.48 L*_V)]^2.46, where L*_V corresponds to M*_V = -22.35, and a QSO is defined to be an object with total nuclear plus host light M_V < -23. This ratio can be interpreted as the probability that a galaxy with luminosity L_V will host a QSO at redshift z ~ 0.26. (Abridged) Comment: 36 pages, 11 figures, LaTeX. Expanded analysis and additional figures. To be published in the Astrophysical Journal, v576, September 1, 2002