A precision measurement of the D0 meson mass has been made using approximately 281 pb(-1) of e+e- annihilation data taken with the CLEO-c detector at the psi(3770) resonance. The exclusive decay D0-->K_{S}phi has been used to obtain M(D0)=1864.847+/-0.150(stat)+/-0.095(syst) MeV. This corresponds to M(D0D*0)=3871.81+/-0.36 MeV, and leads to a well-constrained determination of the binding energy of the proposed D0D*0 molecule X(3872), as Eb=0.6+/-0.6 MeV.