Ubuntu has been offering full disk install-time encryption as an option since Gutsy (7.10). It is available only on the Alternate Install CD -- see the checkbox marked "Check here if you need the alternate desktop CD." on the downloads page http://www.ubuntu.com/getubuntu/download
Also, you're idea of including this functionality on the live CD is a good one. Then I think more people would be aware it is an option, and use it. +1
On a related note, what if sometime in the future you need to use a liveCD to rescue your files which are now on this encrypted drive? Currently I know of no way to do this. The liveCD can only mount unencrypted partitions. I think the liveCD should also have an option to mount encrypted partitions -- so long as you can provide the correct passphrase, of course. See my idea: "Allow LiveCD to access an install-time encrypted partition on HDD."
> the issue is that full disk encryption is not available on the live CD.
Yes, I am aware of this. This is why I added the second part to my comment, re: "you're idea of including this functionality on the live CD is a good one. Then I think more people would be aware it is an option, and use it. +1 "
Upon reading this idea, there was no way for me to know if Dr Small knew that he/she could accomplish full disk encryption already. My intention was simply to be helpful by also including the above information in case he/she or others might benefit from it.
Install from Ubiquity install -> Allow removable media key, full disk encryption (This gets over the HIPAA requirements in the U.S. It is possible that more medical institutions would be willing to use Ubuntu if they meet HIPAA requirements.