To install the Gnome Software Center, open up a terminal window, and type the following command:
sudo apt-get install gnome-software gnome-packagekit

When the Terminal asks if you want to continue, press the ‘Y’ key on your keyboard, then ‘Enter’ again. This command installs two packages – the software center, and the tool that allows the software center to communicate with the Debian system.

Once it’s done downloading and installing everything, you should see a ‘Software’ app in the app drawer. Click on it to open the Gnome Software Center. If the Gnome Software Center App is empty or blank, you may have to restart your Chromebook ~10 times to get it to fully load… at least that’s an issue I initially ran into.