There is a pretty good article over at LWN.net about the state of Trustworthy Computing in Linux, detailing the current and planned support for TPMs in Linux. Prof Sean Smith at Dartmouth created similar applications for Linux back in 2003, when the TPM spec was not yet finalized.
Of the TPM capabilities discussed, "remote attestation" was highlighted significantly in the article. But, keep in mind that Linux, being a monolithic kernel, has more components that would need integrity checking than there are available PCRs in the TPMs. The suggested applications (e.g. checking the integrity of an "email garden" terminal by the remote email server) are a stretch of capabilities.
Also keep in mind that unless coupled with trust at the foundational levels of memory architecture, integrity-sensitive objects could be replaced in memory by any device that has access via DMA. IOMMUs or similar will be required to deliver the solution fully.
And on that note, Cornell's academic OS - Nexus has a much better chance of success, because of the limited number of components that live in kernel space. The fewer the items that need "remote attestation", the more likely the attestation will be meaningful at all. At this point, modern operating systems need to simplify more than they need to accessorize, at least if security is important.