X(3872): Hadronic Molecules in Effective Field Theory

We consider the implications from the possibility that the recently observed state X(3872) is a meson-antimeson molecule. We write an effective Lagrangian consistent with the heavy-quark and chiral symmetries needed to describe X(3872). We claim that if X(3872) is a molecular bound state of D^*0 and anti-D^0 mesons, the heavy-quark symmetry requires the existence of the molecular bound state X_b of B^*0 and anti-B^0 with the mass of 10604 MeV.