Besides google chrome, you can also install chromium on xubuntu for your web browser, in fact you can have both running at the same time on xubuntu, they basically different web browser.
The difference between google chrome and chromium is that google chrome is maintain and developed by google, the source code is closed, while chromium is an open source and maintain by community of developers around the world.
And that's why google chrome doesn't exist on the repository of xubuntu/ubuntu while chromium is available on the repository and ready for you to install.
To install chromium on xubuntu simply run this command:
sudo apt-get install chromium-browser
Just like google chrome, chromium also rely on libindicator7, libappindicator1, and fonts-liberation package, so you might want to install those three packages first if you haven't.
sudo apt-get install libindicator7 libappindicator1 fonts-liberation