The process e(+)e(-) -> gamma chi(cJ) (J = 1, 2) is studied via initial state radiation using 980 fb(-1) of data at and around the Gamma(nS) (n = 1, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetricenergy e(+)e(-) collider. No significant signal is observed except from psi(2S) decays. Upper limits on the cross sections between root s = 3.80 and 5.56 GeV are determined at the 90% credibility level, which range from a 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 gamma chi(cJ).