The structure and phonons of an ordered ice surface, prepared in situ under ultra high vacuum conditions, have been studied by high resolution helium atom scattering. The angular distributions are dominated by sharp hexagonal (1x1) diffraction peaks characteristic of a full bilayer terminated ice Ih crystal. Additional, very broad and weak, p(2.1x2.1) peaks may indicate the presence of small domains of antiphase oriented molecules. An eikonal analysis of the 1x1 peaks is compatible with either a proton disordered or a proton ordered surface with corrugations of 0.76 Angstrom and 0.63 Angstrom, respectively. Inelastic time-of-flight spectra reveal not only a dispersionless phonon branch reported previously at 5.9 meV, but also the first evidence for the surface Rayleigh phonons, which are reproduced well by a Born-von Karman simulation of a full bilayer terminated ice surface using the unmodified force constants derived from neutron scattering bulk phonon measurements. Since the lattice dynamics simulations do not reproduce the dispersionless branch, it is attributed to the vibrations of single water molecules on the ice surface.