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We present a new method for measuring the linear viscoelastic shear moduli of complex fluids. Using photodiode detection of laser light scattered from a thermally excited colloidal probe sphere, we track its trajectory and extract the moduli using a frequency-dependent Stokes-Einstein equation. Spectra obtained for polyethylene oxide in water are in excellent agreement with those found mechanically and using diffusing wave spectroscopy. Since only minute sample volumes are required, this method is well suited for biomaterials of high purity, as we demonstrate with a concentrated DNA solution.