We present the first upper-limit measurement of the branching fractions of the isospin-violating transitions $chi_{c0,2} rightarrow pi^{0} eta_{c}$. The measurements are performed using $106times 10^{6}$ $psi(3686)$ events accumulated with the BESIII
detector at the BEPCII $e^{+}e^{-}$ collider at a center-of-mass energy corresponding to the $psi(3686)$ mass. We obtained upper limits on the branching fractions at a 90% confidence level of $B(chi_{c0} rightarrow pi^{0} eta_{c}) < 1.6 times 10^{-3}$ and $B(chi_{c2} rightarrow pi^{0} eta_{c}) < 3.2 times 10^{-3}$.
