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We demonstrate large cavity-enhanced optical Stark shifts for a single quantum dot (QD) coupled to a photonic crystal cavity. A maximum Stark shift of 20 GHz is observed for a QD detuned by 104 GHz from the cavity mode. These Stark shifts are attained with extremely low cavity field energies of only ten photons. The changes in the QD emission wavelength are monitored via nonresonant transfer between the QD and cavity mode. Experimental results are compared to theoretical predictions based on the solution to the full master equation and found to be in excellent agreement.