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We present a discussion of the science drivers and design approach for a high-resolution, mid-infrared spectrograph for the Thirty-Meter Telescope. The instrument will be integrated with an adaptive optics system optimized for the mid-infrared; as a consequence it is not significantly larger or more complex than similar instruments designed for use on smaller telescopes. The high spatial and spectral resolution possible with such a design provides a unique scientific capability. The design provides spectral resolution of up to 120,000 for the 4.5-25 m region in a cross-dispersed format that provides continuous spectral coverage of up to 2% to 14 micrometers. The basic concept is derived from the successful TEXES mid-infrared spectrograph. To facilitate operation, there are separate imaging channels for the near-infrared and the mid-infrared; both can be used for acquisition and the mid-infrared imaging mode can be used for science imaging and for guiding. Because the spectrograph is matched to the diffraction limit of a 30-m telescope, gains in sensitivity are roughly proportional to the square of the telescope diameter, opening up a volume within the Galaxy a thousand times greater than existing instruments., Published in the Proceedings of the SPIE, Ground-based and Airborne Instrumentation for Astronomy, v6269 n62693U-1 through 62693U-12, 2006. Prepared in collaboration with Naval Research Laboratory, Washington, DC. Prepared in cooperation with University of California, Davis, CA; University of Hawaii, Honolulu, HI; and University of Texas, Austin, TX. The original document contains color images.