Multichannel spectroscopy with millihertz resolution constitutes an attractive strategy for a microwave search for extraterrestrial intelligence (SETI), assuming the transmission of a narrow-band radiofrequency beacon. Such resolution matches the properties of the interstellar medium, and the necessary receiver Doppler corrections provide a high degree of interference rejection. We have constructed a frequency-agile swept receiver with an 8,388,608-channel spectrum analyzer, on-line signal recognition, and multithreshold archiving. A search of 250 Sun-like stars at 1.4 and 2.8 GHz has been carried out with the Arecibo 305-m antenna, and a meridian transit search of the northern sky is in progress at the Harvard-Smithsonian 26-m antenna. Successive spectra of 400 kHz at 0.05 Hz resolution are searched for features characteristic of an intentional narrowband beacon transmission. These spectra are centered on guessable ("magic") frequencies (such as the 21-cm hydrogen hyperfine line), referenced successively to the local standard of rest, the galactic barycenter, and the cosmic blackbody rest frame.