Observation of the Decay $X\left(3872\right)\to {\pi }^{0}{\chi }_{c1}\left(1P\right)$

Using a total of $9.0\text{}\text{}{\mathrm{fb}}^{-1}$ 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 ${e}^{+}{e}^{-}\to \gamma X\left(3872\right)$ with $X\left(3872\right)\to {\pi }^{0}{\chi }_{cJ}$ for $J=0$, 1, 2. We report the first observation of $X\left(3872\right)\to {\pi }^{0}{\chi }_{c1}$, a new decay mode of the $X\left(3872\right)$, with a statistical significance of more than $5\sigma $ for all systematic fit variations. Normalizing to the previously established process ${e}^{+}{e}^{-}\to \gamma X\left(3872\right)$ with $X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi $, we find $B\left(X\left(3872\right)\to {\pi }^{0}{\chi }_{c1}\right)/\phantom{\rule{0ex}{0ex}}B\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)=0.8{8}_{-0.27}^{+0.33}±0.10$, 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.