Using data samples collected at center-of-mass energies of root s=4.009, 4.230, 4.260, and 4.360 GeV with the BESIII detector operating at the BEPCII collider, we perform a search for the process e(+)e(-)->gamma chi(cJ) (J=0, 1, 2) and find evidence for e(+)e(-)->gamma chi(c1) and e(+)e(-)->gamma chi(c2) with statistical significances of 3.0 sigma and 3.4 sigma, respectively. The Born cross sections sigma(B)(e(+)e(-)->gamma chi(cJ)), as well as their upper limits at the 90% confidence level (C.L.) are determined at each center-of-mass energy.
