Observation of the decay $X(3872) \to \pi^0 \chi_{c1}(1P)$

Using a total of 9.0 fb(-1) of e(+)e(-) collision data with center-of-mass energies between 4.15 and 4.30 GeV collected by the BESIII detector, we search for the processes e(+)e(-) gamma X(3872) with X(3872) -> pi(0)chi(cJ) for J = 0, 1, 2. We report the first observation of X(3872) -> pi(0)chi(c1), a new decay mode of the X(3872), with a statistical significance of more than 5 sigma for all systematic fit variations. Normalizing to the previously established process e(+)e(-) -> gamma X(3872) with X(3872) -> pi(+) pi(-) J/psi, we find B(X(3872) -> pi(0)chi(c1))/B(X(3872) -> pi+ pi(-) J/psi) = 0.88(-0.27)(+0.33) +/- 0.10, where the first error is statistical and the second is systematic. We set 90% confidence level upper limits on the corresponding ratios for the decays to pi(0)chi(c0) and pi(0)chi(c2) of 19 and 1.1, respectively.