How can I enable silent automatic updates for Google Chrome?

1. Install unattended upgrades:

   sudo apt-get install unattended-upgrades
   

2. Enable unattended updates on the Google Chrome repo by editing the unattended upgrades list and adding the Google Chrome repo in it:

   sudo gedit /etc/apt/apt.conf.d/50unattended-upgrades
   

   Add "Google\, Inc.:stable"; to the allowed origins:

   Unattended-Upgrade::Allowed-Origins {
       "${distro_id} ${distro_codename}-security";
   //  "${distro_id} ${distro_codename}-updates";
   //  "${distro_id} ${distro_codename}-proposed";
   //  "${distro_id} ${distro_codename}-backports";
    "Google LLC:stable";
   };
   

3. Test

   Use sudo unattended-upgrade --dry-run to test, if all came clear you should be having updates to Google Chrome installed without any intervention from you.

To check that it's working tail the log after the dry run:

cat /var/log/unattended-upgrades/unattended-upgrades.log

and you should see something along the lines of this in your log:

2011-10-11 18:03:23,292 INFO Allowed origins are: ['o=Ubuntu,a=oneiric-security', 'o=Google, Inc.,a=stable']

You can change the configuration of the unattended updates by editing the file /etc/apt/apt.conf.d/10periodic, options for the configuration are in the /etc/cron.daily/apt script header. Read them to configure the frequency of the unattended updates.