A collision between two molecular clouds is one possible candidate for high-mass star formation. The HII region RCW 36, located in the Vela molecular ridge, contains a young star cluster with two O-type stars. We present new CO observations of RCW 36 with NANTEN2, Mopra, and ASTE using $^{12}$CO($J$ = 1-0, 2-1, 3-2) and $^{13}$CO($J$ = 2-1) line emissions. We have discovered two molecular clouds lying at the velocities $V_mathrm{LSR} sim$5.5 and 9 km s$^{-1}$. Both clouds are likely to be physically associated with the star cluster, as verified by the good spatial correspondence among the two clouds, infrared filaments, and the star cluster. We also found a high intensity ratio of $sim$0.6-1.2 for CO $J$ = 3-2 / 1-0 toward both clouds, indicating that the gas temperature has been increased due to heating by the O-type stars. We propose that the O-type stars in RCW 36 were formed by a collision between the two clouds, with a relative velocity separation of 5 km s$^{-1}$. The complementary spatial distributions and the velocity separation of the two clouds are in good agreement with observational signatures expected for O-type star formation triggered by a cloud-cloud collision. We also found a displacement between the complementary spatial distributions of the two clouds, which we estimate to be 0.3 pc assuming the collision angle to be 45$^{circ}$ relative to the line-of-sight. We estimate the collision timescale to be $sim$10$^5$ yr. It is probable that the cluster age by Ellerbroek et al. (2013b) is dominated by the low-mass members which were not formed under the triggering by cloud-cloud collision, and that the O-type stars in the center of the cluster are explained by the collisional triggering independently from the low-mass star formation.
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