The GMT-Consortium Large Earth Finder (G-CLEF) is a fiber fed, optical echelle spectrograph that has been selected as a first light instrument for the Giant Magellan Telescope (GMT) currently under construction at the Las Campanas Observatory in Chile's Atacama desert region. We designed G-CLEF as a general-purpose echelle spectrograph with precision radial velocity (PRV) capability used for exoplanet detection. The radial velocity (RV) precision goal of GCLEF is 10 cm/sec, necessary for detection of Earth-sized planets orbiting stars like our Sun in the habitable zone. This goal imposes challenging stability requirements on the optical mounts and the overall spectrograph support structures. Stability in instruments of this type is typically affected by changes in temperature, orientation, and air pressure as well as vibrations caused by telescope tracking. For these reasons, we have chosen to enclose G-CLEF's spectrograph in a thermally insulated, vibration isolated vacuum chamber and place it at a gravity invariant location on GMT's azimuth platform. Additional design constraints posed by the GMT telescope include: a limited space envelope, a thermal emission ceiling, and a maximum weight allowance. Other factors, such as manufacturability, serviceability, available technology and budget are also significant design drivers. All of the previously listed considerations must be managed while ensuring that performance requirements are achieved. In this paper, we discuss the design of G-CLEF's optical mounts and support structures including technical choices made to minimize the system's sensitivity to thermal gradients. A more general treatment of the properties of G-CLEF can be found elsewhere in these proceedings1. We discuss the design of the vacuum chamber which houses the irregularly shaped optical bench and optics while conforming to a challenging space envelope on GMT's azimuth platform. We also discuss the design of G-CLEF's insulated enclosure and thermal control systems which maintain the spectrograph at milli-Kelvin level stability while simultaneously limiting the maximum thermal emission into the telescope dome environment. Finally, we discuss G-CLEF's front-end assembly and fiber-feed system as well as other interface challenges presented by the telescope, enclosure and neighboring instrumentation.