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Using 9.0 fb−1 of e+e− collision data collected at center-of-mass energies from 4.178 to 4.278 GeV with the BESIII detector at the BEPCII collider, we perform the first search for the radiative transition χc1(3872)→γψ2(3823). No χc1(3872)→γψ2(3823) signal is observed. The upper limit on the ratio of branching fractions B(χc1(3872)→γψ2(3823),ψ2(3823)→γχc1)/B(χc1(3872)→π+π−J/ψ) is set as 0.075 at the 90\% confidence level. Our result contradicts theoretical predictions under the assumption that the χc1(3872) is the pure charmonium state χc1(2P).