We describe the design, fabrication, and testing of a monolithic interferometer consisting entirely of optically contacted fused-silica optical elements that are assembled, adjusted, and permanently bonded in place. The interferometer is part of a spatial heterodyne spectrometer (SHS) [SHIMMER (Spatial Heterodyne Imager for Mesospheric Radicals)] that will be used for near-ultraviolet high-spectral-resolution limb imaging of OH solar resonance fluorescence from low Earth orbit aboard the satellite STPSat-1 scheduled for launch in 2006. The stability of the monolith coupled with the relaxed tolerances on optical quality and alignment inherent to SHS make this new instrument extremely robust and especially attractive for applications in harsh environments.