Using 980.6 $rm fb^{-1}$ of data collected with the Belle detector operating at the KEKB asymmetric-energy $e^+e^-$ collider, we present a measurement of the branching fraction of the singly Cabibbo-suppressed decay $Lambda_c^+ to p omega$. A clear $Lambda_c^+$ signal is observed for $Lambda_c^+ to p omega$ with a statistical significance of 9.1 standard deviations, and we measure the ratio of branching fractions ${cal B}(Lambda_c^+ to p omega)/{cal B}(Lambda_c^+ to p K^- pi^+) = (1.32 pm 0.12 (rm stat) pm 0.10 (rm syst))times 10^{-2}$, from which we infer the branching fraction ${cal B}(Lambda_c^+ to p omega) = (8.27 pm 0.75 (rm stat) pm 0.62 (rm syst) pm 0.42 (rm ref))times 10^{-4}$. The first quoted uncertainty is statistical, the second systematic, and the third from the reference mode $Lambda_c^+ to p K^- pi^+$.
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