Traditional technologies for far-infrared (FIR) spectroscopy generally involve bulky dispersive optics. Integrated filter bank spectrometers promise more compact designs, but implementations using superconducting transmission line networks become lossy at terahertz frequencies. We describe a novel on-chip spectrometer architecture designed to extend this range. A filter bank spectrometer is implemented using vacuum waveguide etched into a silicon wafer stack. A single trunk line feeds an array of resonant cavities, each coupled to a kinetic inductance detector fabricated on an adjacent wafer. We discuss the design and fabrication of a prototype implementation, initial test results at ambient temperature, and prospects for future development.