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We present a new technique for detecting scattered starlight from transiting,close-orbiting extrasolar giant planets (CEGPs) that has the virtues ofsimplicity, robustness, linearity, and model-independence. Given a series ofstellar spectra obtained over various phases of the planetary orbit, the goalis to measure the strength of the component scattered by the planet relative tothe component coming directly from the star. We use two complementarystrategies, both of which rely on the predictable Doppler shifts of bothcomponents and on combining the results from many spectral lines and manyexposures. In the first strategy, we identify segments of the stellar spectrumthat are free of direct absorption lines and add them after Doppler-shiftinginto the planetary frame. In the second strategy, we compare the distributionof equivalent-width ratios of the scattered and direct components. Bothstrategies are calibrated with a ``null test'' in which scrambled Dopplershifts are applied to the spectral segments. As an illustrative test case, weapply our technique to spectra of HD 209458 taken when the planet was nearopposition (with orbital phases ranging from 11 to 34$\arcdeg$, where0$\arcdeg$ is at opposition), finding that the planet-to-star flux ratio is$(1.4 \pm 2.9)\times10^{-4}$ in the wavelength range 554$-$681 nm. Thiscorresponds to a geometric albedo of $0.8 \pm 1.6$, assuming the phase functionof a Lambert sphere. Although the result is not statistically significant, theachieved sensitivity and relatively small volume of data upon which it is basedare very encouraging for future ground-based spectroscopic studies of scatteredlight from transiting CEGP systems.

A Technique for Detecting Starlight Scattered from Transiting Extrasolar Planets with Application to HD 209458b