Based on data samples collected with the BESIII detector at the BEPCII collider at nine center of mass energies from 4.21 to 4.42 GeV, we search for the production of e^{+}e^{-}→ωχ_{cJ} (J=0, 1, 2). The process e^{+}e^{-}→ωχ_{c0} is observed for the first time, and the Born cross sections at sqrt[s]=4.23 and 4.26 GeV are measured to be (55.4±6.0±5.9) and (23.7±5.3±3.5) pb, respectively, where the first uncertainties are statistical and the second are systematic. The ωχ_{c0} signals at the other seven energies and the e^{+}e^{-}→ωχ_{c1} and ωχ_{c2} signals are not significant, and the upper limits on the cross sections are determined. By examining the ωχ_{c0} cross section as a function of center of mass energy, we find that it is inconsistent with the line shape of the Y(4260) observed in e^{+}e^{-}→π^{+}π^{-}J/ψ. Assuming the ωχ_{c0} signals come from a single resonance, we extract the mass and width of the resonance to be (4230±8±6) MeV/c^{2} and (38±12±2) MeV, respectively, and the statistical significance is more than 9σ.