I doubt that the chest is full you are more likely to have a file that exceeds the Program Settings (right click the avast 'a' icon) Chest, Maximum file size to send and adjust your settings.
This is preferable to deleting to make room as a quick fix.
Doing a system restore won't touch the files in the chest, they are infected files in a protected area.
To delete files in the chest you must first open the chest, right click the avast 'a' icon, select avast! virus chest, Infected Files section, now see below.
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There is no rush to delete anything from the chest, a protected area where it can do no harm. Anything that you send to the chest you should leave there for a few weeks. If after that time you have suffered no adverse effects from moving these to the chest, scan them again (inside the chest) and if they are still detected as viruses, delete them.