  In this study we present the first theoretical calculation of the form factor
of the $\chi_{c0}(1P) \rar J/\psi \gamma $ and $\chi_{b0}(1P) \rightarrow
\Upsilon(1S) \gamma $ decays in the frame work of QCD sum rules. We also find
branching ratio ${\cal B}_r(\chi_{c0}(1P) \rightarrow J/\psi
\gamma)=(1.07\times \pm 0.14) \times 10^{(-2)} $ which is in agreement with the
experimental data. Furthermore, we estimate the $\Gamma_{tot}(\chi_{b0}(1P))
=5.5\pm 0.5 $ MeV, where experimental bound for full width of $\chi_{b0}$ is
$\Gamma_{tot}(\chi_{b0}(1P)) <6 $ MeV.
