We study the atomic structure of the Si(111)3ϫ2-Ba surface using low-energy electron diffraction ͑LEED͒, scanning tunneling microscopy ͑STM͒, and ab initio calculations. A 3ϫ2 periodicity is observed not only in STM but also in LEED. From dual-bias STM imaging and total-energy calculations, the recently proposed honeycomb chain-channel ͑HCC͒ structure ͓G. Lee et al., Phys. Rev. Lett. 87, 056104 ͑2001͔͒ is confirmed to be the most favorable among various candidate structures. Calculations varying Ba-Ba distance in the channel show that the Ba atoms interact repulsively. Diffusion of Ba atoms along the channel, occurring in a concerted manner, is found to be unlikely at room temperature. This is consistent with the STM observation that the Ba atoms occupy specific sites. However, some static disorder in site occupation is observed and shown to be energetically probable. We suggest that the Si͑111͒ surface has a tendency towards the 3ϫ1-HCC reconstruction when one electron per 3ϫ1 unit are supplied and fully saturate the Si dangling bonds.