Based on data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies $sqrt{s} >$ 4.4 GeV, the processes $e^+e^- rightarrow omega chi_{c1,2}$ are observed for the first time. With an integrated luminosity of $1074 pb^{-1}$ near $sqrt{s} =$ 4.42 GeV, a significant $omega chi_{c2}$ signal is found, and the cross section is measured to be $(20.9 pm 3.2 pm 2.5)pb$. With $567 pb^{-1}$ near $sqrt{s} =$ 4.6 GeV, a clear $omega chi_{c1}$ signal is seen, and the cross section is measured to be $(9.5 pm 2.1 pm 1.3) pb$, while evidence is found for an $omega chi_{c2}$ 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 $omega chi_{c2}$ cross section, an enhancement is seen around $sqrt{s} =$ 4.42 GeV. Fitting the cross section with a coherent sum of the $psi(4415)$ Breit-Wigner function and a phase space term, the branching fraction $mathcal{B}(psi(4415)toomegachi_{c2})$ is obtained to be of the order of $10^{-3}$.
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