  We consider pion interactions in an effective field theory of the narrow
resonance X(3872), assuming it is a weakly bound molecule of the charm mesons
D^{0} \bar D^{*0} and D^{*0} \bar D^{0}. Since the hyperfine splitting of the
D^{0} and D^{*0} is only 7 MeV greater than the neutral pion mass, pions can be
produced near threshold and are non-relativistic. We show that pion exchange
can be treated in perturbation theory and calculate the next-to-leading-order
correction to the partial decay width \Gamma[X \to D^0 \bar D^{0} \pi^0].
