Both the mass (just below the D * 0D0 threshold) and the likely quantum numbers (J P C = 1 ++ ) of the X(3872) suggest that it is either a weakly-bound hadronic "molecule" (X(3872 ∼ 1/ √ 2[D * 0D0 +D * 0 D 0 ]) or a virtual state of charmed mesons. Assuming the X(3872) is a weaklybound molecule, the scattering of neutral D and D * mesons off the X(3872) can be predicted from the X(3872) binding energy. We calculate the phase shifts and cross section for scattering of D 0 and D * 0 mesons and their antiparticles off the X(3872) in an effective field theory for short-range interactions. This provides another example of a three-body process, along with those in nuclear and atomic systems, that displays universal properties. It may be possible to extract the scattering within the final state interactions of B c decays and/or other LHC events. * Electronic address: canham@itkp.uni-bonn.de † Electronic address: hammer@itkp.uni-bonn.de ‡ Electronic address: rps@phy.duke.edu 1 Note, however, that J P C = 2 −+ cannot be experimentally excluded at present.