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We present 4 years of spectrophotometric monitoring data for two radio-quietquasars, PG 0804+762 and PG 0953+414, with typical sampling intervals ofseveral months. Both sources show continuum and emission line variations. Thevariations of the H$\beta$ line follow those of the continuum with a time lag,as derived from a cross-correlation analysis, of 93$\pm$30 days for PG 0804+762and 111$\pm$55 days for PG 0953+414. This is the first reliable measurement ofsuch a lag in active galactic nuclei with luminosity $L>10^{45}$ erg s$^{-1}$.The broad line region (BLR) size that is implied is almost an order ofmagnitude larger than that measured in several Seyfert 1 galaxies and isconsistent with the hypothesis that the BLR size grows as $L^{0.5}$.Comment: 5 pages, LaTeX (including aas2pp4 and epsf), including 4 EPS figures.  Accepted for publication in Astrophysical Journal Letter

Measurement of the Broad-Line Region Size in Two Bright Quasars