Measurement of sigma chi c2 B(chi c2-->J/psi gamma)/sigma chi c1 B(chi c1 -->J/psi gamma) in pp collisions at square root s=1.96 TeV.

We measure the ratio of cross section times branching fraction, Rp=sigma chi c2 B(chi c2-->J/psi gamma)/sigma chi c1 B(chi c1-->J/psi gamma), in 1.1 fb(-1) of pp collisions at square root s=1.96 TeV. This measurement covers the kinematic range pT(J/psi)>4.0 GeV/c, |eta(J/psi)<1.0, and pT(gamma)>1.0 GeV/c. For events due to prompt processes, we find Rp=0.395+/-0.016(stat)+/-0.015(syst). This result represents a significant improvement in precision over previous measurements of prompt chi c1,2 hadro production.