Project Server has been available as a cloud-based service since 2003 through hosting partners, and therefore is an enterprise product with one of the longest histories of online success – through three full versions.
www.ProjectHosts.com has been hosting Project Server the longest and has the biggest customer base including US Defense agencies (their environment is extremely secure and reliable). Sign up for a free trial account here: https://secure.projecthosts.com/PB_Registration.asp?Rep=mikekr
Two other hosting partners are listed here: http://www.microsoft.com/project/en/us/on-demand-hosting.aspx
Like many other Microsoft software, Project will eventually be available in the Microsoft hosting environment. The timeline for Project in the BPOS suite has not been announced, but we expect more information in the coming months.