Using a data sample corresponding to an integrated luminosity of 11.3 fb-1 collected at center-of-mass energies from 4.23 to 4.70 GeV with the BESIII detector, we measure the product of the e+e-→π+π-ψ2(3823) cross section and the branching fraction B[ψ2(3823)→γχc1]. For the first time, resonance structure is observed in the cross section line shape of e+e-→π+π-ψ2(3823) with significances exceeding 5σ. A fit to data with two coherent Breit-Wigner resonances modeling the s-dependent cross section yields M(R1)=4406.9±17.2±4.5 MeV/c2, Γ(R1)=128.1±37.2±2.3 MeV, and M(R2)=4647.9±8.6±0.8 MeV/c2, Γ(R2)=33.1±18.6±4.1 MeV. Though weakly disfavored by the data, a single resonance with M(R)=4417.5±26.2±3.5 MeV/c2, Γ(R)=245±48±13 MeV is also possible to interpret data. This observation deepens our understanding of the nature of the vector charmoniumlike states. The mass of the ψ2(3823) state is measured as (3823.12±0.43±0.13) MeV/c2, which is the most precise measurement to date. © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.