What filesystem type is the external drive formatted with?
If it's "Ext4" (Ext3 or Ext2), do this after you plug in the drive and it's mounted to "/media/chris":
sudo chown -R chris: /media/chris/259e8ba4-8c54-43ad-9dc0-2a1ed024910e
Try backup again -- it should work now.
If it's some other formatting let us know which it is.
Additional Note:You may want to label that external drive's partition so it ends up easier to read.
- Open GParted (Menu->System->Partition Drives)
- Rt-clk the external drive's partition and choose "Unmount"
- Rt-clk it again and choose "Label"
- Type in a short, descriptive label -- eg. Backups
- Click "Apply" button (or Edit->Apply All Operations)
- Rt-clk and choose "Mount", then close GParted
Now if you look in file manager (and when you plug it in in the future) it should read as "/media/chris/Backups" instead of that long string of numbers and letters.
P.s. If for some reason the above did not work, (with the external drive plugged-in and mounted) open a terminal and enter these two commands:
sudo blkid -c /dev/null
ls -l /media/chris
Copy/Paste the full results back here.