Water (H2O) ice is an important solid constituent of many astrophysical environments. To comprehend the role of such ices in the chemistry and evolution of dense molecular clouds and comets, it is necessary to understand the freeze-out, potential surface reactivity, and desorption mechanisms of such molecular systems. Consequently, there is a real need from within the astronomical modelling community for accurate empirical molecular data pertaining to these processes. Here we give the first results of a laboratory programme to provide such data. Measurements of the thermal desorption of H2O ice, under interstellar conditions, are presented. For ice deposited under conditions that realistically mimic those in a dense molecular cloud, the thermal desorption of thin films (~50 molecular layers) is found to occur with zero order kinetics characterised by a surface binding energy, E_{des}, of 5773 +/- 60 K, and a pre-exponential factor, A, of 10^(30 +/- 2) molecules cm^-2 s^-1. These results imply that, in the dense interstellar medium, thermal desorption of H2O ice will occur at significantly higher temperatures than has previously been assumed. ; Comment: 9 pages, 4 figures, accepted for publication in MNRAS