Radiometer spectrometers are used in millimeter-wave radio astronomy for the spectral measurement of molecular rotational transitions. The spectrum of interest spans 10's of GHz and the measurement time is large in order to obtain useful signal-to-noise ratio. The low power/channel and simplicity of acousto-optic technology has led to the current development of acousto-optic spectrometers (AOS) with 1 GHz bandwidth and 1000 channels. Additional AOS bandwidth and channelization is needed to increase spectral coverage, reduce overall data acquisition time, and accommodate multibeam antennas. A multichannel acousto-optic spectrometer (MCAOS) for radio astronomy spectroscopy applications has been developed with 4 channels that can process signals from 4 separate sources simultaneously. The bandwidth of each channel is 1 GHz and the frequency resolution is 1 MHz, providing simultaneous processing over 4,000 1 MHz channels. The design and initial performance of this instrument is described. Design considerations for future wider bandwidth MCAOS's are also presented.