The process $e^+e^- to gammachi_{cJ}$ ($J$=1, 2) is studied via initial state radiation using 980 fb$^{-1}$ of data at and around the $Upsilon(nS)$ ($n$=1, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-
$ collider. No significant signal is observed except from $psi(2S)$ decays. Upper limits on the cross sections between $sqrt{s}=3.80$ and $5.56~{rm GeV}$ are determined at the 90% credibility level, which range from few pb to a few tens of pb. We also set upper limits on the decay rate of the vector charmonium [$psi(4040$), $psi(4160)$, and $psi(4415)$] and charmoniumlike [$Y(4260)$, $Y(4360)$, and $Y(4660)$] states to $gammachi_{cJ}$.
