The Solar Wind ANisotropies (SWAN) all-sky hydrogen Lyα camera on the SOlar and Heliospheric Observer (SOHO) satellite observed the hydrogen coma of comet C/2012 S1 (ISON) for most of the last month of its activity from 2013 October 24 to November 24, ending just 4 days before perihelion and its final disruption. The water production rate of the comet was determined from these observations. SOHO has been operating in a halo orbit around the Earth-Sun L1 Lagrange point since its launch in late 1995. Most water vapor produced by comets is ultimately photodissociated into two H atoms and one O atom producing a huge hydrogen coma that is routinely observed in the daily SWAN images in comets of sufficient brightness. Water production rates were calculated from 22 images over most of the last month of the pre-perihelion apparition. The water production rate increased very slowly on average from October 24.9 until November 12.9, staying between 1.8 and 3.4 × 10²⁸ s^-1, after which it increased dramatically, reaching 1.6 to 2 × 10³⁰ s^-1 from November 21.6 to 23.6. It was not detected after perihelion on December 3.7 when it should have been visible. We examine the active surface area necessary to explain the water production rate and its variation and are able to place constraints on the physical size of the original nucleus necessary to account for the large amount of activity from November 12.9 and until just before perihelion.