We study the prospects for constraining dark energy at very high redshift with the Sandage-Loeb test—a measurement of the evolution of cosmic redshift obtained by taking quasar spectra at sufficiently separated epochs. This test is unique in its coverage of the “redshift desert,” corresponding roughly to redshifts between 2 and 5, where other dark energy probes are unable to provide useful information about the cosmic expansion history. Extremely large telescopes planned for construction in the near future, with ultrahigh resolution spectrographs (such as the proposed CODEX), will indeed be able to measure cosmic redshift variations of quasar Lyman-α absorption lines over a period as short as ten years. We find that these measurements can constrain nonstandard and dynamical dark energy models with high significance and in a redshift range not accessible with future dark energy surveys. As the cosmic signal increases linearly with time, measurements made over several decades by a generation of patient cosmologists may provide definitive constraints on the expansion history in the era that follows the dark ages but precedes the time when standard candles and rulers come into existence.