Googling
linux split file the first hit I get says how to split and combine
split –bytes=500m /path/to/large/file /path/to/output/file/prefix
such as
split -bytes=500m /home/YOURACCOUNT/public_html/the_backup.tgz /home/YOURACCOUNT/public_html/backup_split
It may take several tries to get it right. 500m is supposed to give you 500MB chunks -- you could also try 1000m.
I presume that you know where to find
cron in your control panel. Just make it a one-time job firing off in a few minutes from now (set minutes, leave all other fields
* is the easiest way). After giving it a chance to run, check that it did, and delete the cron job so it isn't run every hour for the rest of eternity.