The potential of mean force between two large parallel hydrophobic oblate ellipsoidal plates in liquid water is determined by molecular dynamics. Each ellipsoid displaces approximately 40 water molecules and has major and minor axes of 3.1 and 9.3 Angstrom, respectively, has a surface area of 650 Angstrom(2), and interacts repulsively with the solvent water molecules. The potential of mean force is calculated from thermodynamic perturbation theory for a series of decreasing plate separations, using constant-pressure molecular dynamics. As the plates are moved together, they are first separated by three water layers and then by two, but for shorter distances, a dewetting transition occurs, and one water layer is never observed despite the fact that one can fit. As the plates are brought together, there is a corresponding weak oscillation in the potential of mean force corresponding to the removal Of each water layer until the dewetting transition takes place, and for closer separations, the surrounding water molecules induce a constant average attractive force of 25 (kJ/mol)/Angstrom between the plates. This hydrophobic attraction is largely entropic in character, and the potential of mean force is found to be proportional to the area of the water-vacuum surface in this dewetting regime. The constant of proportionality is found to be smaller than the gas-liquid surface tension of the water model used. There is a very strong short-range driving force toward contact pairing.