  Using a 478 pb$^{-1}$ data sample collected with the BESIII detector
operating at the BEPCII storage ring at a center-of-mass energy of
$\sqrt{s}=4.009$ GeV, the production of $e^{+}e^{-}\to \eta J\psi$ is observed
for the first time with a statistical significance of greater than $10\sigma$.
The Born cross section is measured to be $(32.1\pm 2.8 \pm 1.3)$ pb, where the
first error is statistical and the second systematic. Assuming the $\eta J\psi$
signal is from a hadronic transition of the $\psi(4040)$, the fractional
transition rate is determined to be ${\cal B}(\psi(4040)\to \eta J\psi)=(5.2\pm
0.5\pm 0.2\pm 0.5)\times 10^{-3}$, where the first, second, and third errors
are statistical, systematic, and the uncertainty from the $\psi(4040)$ resonant
parameters, respectively. The production of $e^{+}e^{-} \to \pi^0 J\psi$ is
searched for, but no significant signal is observed, and ${\cal
B}(\psi(4040)\to \pi^0 J\psi) < 2.8 \times 10^{-4}$ is obtained at the 90%
confidence level.
