Hi drfisch,
The virus chest is what other anti-malware programs refer to as quarantine: the malware is inactive but can be restotred in the rare event that a legitimate application is wrongly identified as malware.
It is not necessary to delete files in the chest to complete the cleaning process. In fact, you would be well advised to leave files in the chest for several weeks just to be certain that they have been correctly identified.
avast! also stores copies of some important system files in the chest (under a separate tab) so that these files can be restored if they become corrupted. Do not think that avast! has incorrectly removed some important system files: this is not the case.
As Spiritsongs has said, as you've found malware on the computer, it would be a good idea to run a scan with Ewido.
I also recommend Ad-Aware and Spybot Search & Destroy:
http://www.lavasoftusa.com/software/adaware/http://www.safer-networking.org/Don't neglect to update both programs before scanning.
You also need to ensure that your OS and applications are up to date.
Visit Microsoft update and check that you have the latest updates.
You will need to update other applications too: Quicktime had a critical vulnerability recently, for one.
If you have Firefox 1.5, updates should come through automatically: check that you have the latest version.
If you have Sun Java, that's had critical vulnerabilities too and will need updating.