Based on data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies s>4.4 GeV, the processes e+e-→ωχc1,2 are observed for the first time. With an integrated luminosity of 1074 pb-1 near s=4.42 GeV, a significant ωχc2 signal is found, and the cross section is measured to be (20.9±3.2±2.5) pb. With 567 pb-1 near s=4.6 GeV, a clear ωχc1 signal is seen, and the cross section is measured to be (9.5±2.1±1.3) pb, while evidence is found for an ωχc2 signal. The first errors are statistical, and the second are systematic. Due to low luminosity or low cross section at other energies, no significant signals are observed. In the ωχc2 cross section, an enhancement is seen around s=4.42 GeV. Fitting the cross section with a coherent sum of the ψ(4415) Breit-Wigner function and a phase-space term, the branching fraction B(ψ(4415)→ωχc2) is obtained to be of the order of 10-3.