Ultra-Compact, Superconducting Spectrometer-on-a-Chip at Submillimeter WavelengthsSmall size, wide spectral bandwidth, and highly multiplexed detector readout are required to develop powerful multi-beam spectrometers for high-redshift observations. Currently available spectrometers at these frequencies are large and bulky. The grating sizes for these spectrometers are prohibitive. This fundamental size issue is a key limitation for space-based spectrometers for astrophysics applications. A novel, moderate-resolving-power (R-700), ultra-compact spectrograph-on-a-chip for millimeter and submillimeter wavelengths is the solution.