I have then deleted the virus or trojan from the chest only to find it ends up back on my computer.
Deleting things from the virus chest does not put the files back on your system.
Also, there are times when avast notifies me of a virus or a trojan and then when I try to move to chest or delete avast puts up an alert that the "file" or whatever is in use and can't be moved or deleted..and this will go on and on.
If you have a NT based system you can avoid this by running a boottime scan. Or disable the process/application first and than move/delete the infected items.

To clean your system thoroughly, click on the link in my signature and follow the instructions in the malware removal section.