By using a reflective-echelon-based electro-optic sampling technique and a fast detector, we develop a two-dimensional terahertz (THz) spectrometer capable of shot-to-shot balanced readout of THz waveforms at a full 1-kHz repetition rate. To demonstrate the capabilities of this new detection scheme for high-throughput applications, we use gas-phase acetonitrile as a model system to acquire two-dimensional THz rotational spectra. The results show a two-order-of-magnitude speedup in the acquisition of multidimensional THz spectra when compared to conventional delay-scan methods while maintaining accurate retrieval of the nonlinear THz signal. Our report presents a feasible solution for bringing the technique of multidimensional THz spectroscopy into widespread practice.