A direct measurement of the universe's expansion history could be made by observing in real time the evolution of the cosmological redshift of distant objects. However, this would require measurements of Doppler velocity drifts of approximately 1 centimeter per second per year, and astronomical spectrographs have not yet been calibrated to this tolerance. We demonstrated the first use of a laser frequency comb for wavelength calibration of an astronomical telescope. Even with a simple analysis, absolute calibration is achieved with an equivalent Doppler precision of approximately 9 meters per second at approximately 1.5 micrometers-beyond state-of-the-art accuracy. We show that tracking complex, time-varying systematic effects in the spectrograph and detector system is a particular advantage of laser frequency comb calibration. This technique promises an effective means for modeling and removal of such systematic effects to the accuracy required by future experiments to see direct evidence of the universe's putative acceleration.