The deuterium-to-hydrogen (D/H) ratio in strongly bound water or hydroxyl groups in ancient martian clays retains the imprint of the water of formation of these minerals. Curiosity's Sample Analysis at Mars (SAM) experiment measured thermally evolved water and hydrogen gas released between 550 degrees and 950 degrees C from samples of Hesperian-era Gale crater smectite to determine this isotope ratio. The D/H value is 3.0 (+/- 0.2) times the ratio in standard mean ocean water. The D/H ratio in this similar to 3-billion-year-old mudstone, which is half that of the present martian atmosphere but substantially higher than that expected in very early Mars, indicates an extended history of hydrogen escape and desiccation of the planet.