Ok. I had this same problem, and it was caused by installing Xubuntu-destop (=XFCE, =Thunar) on top of Ubuntu back when I was not acclimated to Unity yet. Thunar brings in a package that causes this exact problem, you can read the link I posted above.
The preferances are correct as the files do save to the downloads folder, the permissions for the folder is drwxr-xr-x and I have already done a removal and reinstall of chromium to try an solve this problem before
I don't believe removal of Chromium through Synaptic, Software Manager, or apt automatically removes the config folder. It might be worth verifying this though.
Asus G73JH - Intel Core i7/Radeon HD5870 - No Linux distro at the moment
MSI B85-G41 Mainboard with Intel Core i3 Proc - Ubuntu 16.04 "Xenial" server edition/Kodi 17.3 "Krypton"
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