A chirped millimeter-wave pulse generates a coherent, oscillating electric field signal, E(t), by polarizing Rydberg-Rydberg transitions in a ~5K ensemble of atoms or molecules. All transitions that lie within a 35 GHz bandwidth are polarized by this pulse. The resultant E(t) signal is heterodyne-detected in the time domain by mixing with a local oscillator. The Fourier Transform of E(t) yields ~100 kHz resolution lineshapes of individual transitions with meaningful relative intensities and phases. The buffer gas cooled ablation source (developed in the John Doyle and David DeMille laboratories) produces a beam that is >100 times brighter and 10 times slower than a typical Smalley-type supersonic jet ablation source. The marriage of chirped pulse millimeter-wave spectroscopy with the buffer gas cooled source yields an increase in spectral velocity (number of resolution elements recorded per unit time) of a factor of one million! The value of this unique spectrometer is not limited to obtaining enormous data sets of high precision Rydberg-Rydberg transition frequencies. It is possible, in a single pulse, to obtain the time-dependent E(t) amplitude and corresponding frequency domain spectrum of single transitions. These amplitudes and spectra display extremely strong, coherent, many-particle, cooperative effects, including superradiant emission, frequency chirps, and level shifts. Demodulation of the ~280 GHz E(t) signal generated by a single excitation pulse, reveals the complete amplitude vs. time response of a many-particle two-level system of unprecedented optical thickness, owing to the nearly kilo-Debye transition moments of n~30 ¿n=1Rydberg-Rydberg transitions and the large number density (~107 cm-3) of selectively laser-populated Rydberg states. Even a simple qualitative comparison of these signals with a full many-body calculation confirms that the experiment explores a deeply cooperative regime and shows superradiance-like signals more clearly than seen in experiments before.