  We study the direct production of the $J^{PC}=1^{++}$ charmonium state
$\chi_{c1}(1P)$ in electron-positron annihilation by carrying out an energy
scan around the mass of the $\chi_{c1}(1P)$. The data were collected with the
BESIII detector at the BEPCII collider. An interference pattern between the
signal process $e^+e^-\to \chi_{c1}(1P) \to \gamma J/\psi\to\gamma\mu^+\mu^-$
and the background processes $e^+e^-\to \gamma_{\mathrm{ISR}}
J/\psi\to\gamma_{\rm{ISR}}\mu^+\mu^-$ and
$e^+e^-\to\gamma_{\rm{ISR}}\mu^+\mu^-$ are observed by combining all the data
samples. The $\chi_{c1}(1P)$ signal is observed with a significance of
5.1$\sigma$. This is the first observation of a $C$-even state directly
produced in $e^+e^-$ annihilation. The electronic width of the $\chi_{c1}(1P)$
resonance is determined to be $\Gamma_{ee}=(0.12^{+0.13}_{-0.08})~\mathrm{eV}$,
which is of the same order of magnitude as theoretical calculations.
