1. The document describes a chirp readout technique for kinetic inductance detectors (KIDs) that uses frequency sweeps to simultaneously read out thousands of channels. 2. It achieves high multiplexing factors of up to 4000 channels per octave of bandwidth by performing fast Fourier transforms on short segments of the readout signal. 3. Test results show the technique can achieve noise equivalent powers as low as 3 milli-Hz/sqrt(Hz), allowing high sensitivity measurements of line intensities and widths for over 100 detectors.