We have developed a new thermodynamic theory of the quasiliquid layer, which has been shown to be effective in modeling the phenomenon in a number of molecular systems. Here we extend our analysis to H(2)O ice, which has obvious implications for environmental and atmospheric chemistry. In the model, the liquid layer exists in contact with an ice defined as a two-dimensional lattice of sites. The system free energy is defined by the bulk free energies of ice I(h) and liquid water and is minimized in the grand canonical ensemble. An additional configurational entropy term arises from the occupation of the lattice sites. Furthermore, the theory predicts that the layer thickness as a function of temperature depends only on the liquid activity. Two additional models are derived, where slightly different approximations are used to define the free energy. With these two models, we illustrate the connection between the quasiliquid phenomenon and multilayer adsorption and the possibility of a two-dimensional phase transition connecting a dilute low coverage phase of adsorbed H(2)O and the quasiliquid phase. The model predictions are in agreement with a subset of the total suite of experimental measurements of the liquid thickness on H(2)O ice as a function of temperature. The theory indicates that the quasiliquid layer is actually equivalent to normal liquid water, and we discuss the impact of such an identification. In particular, observations of the liquid layer to temperatures as low as 200 K indicate the possibility that the quasiliquid is, in fact, an example of deeply supercooled normal water. Finally, we briefly discuss the obvious extension of the pure liquid theory to a thermodynamic theory of interfacial solutions on ice in the environment.