How do I enter a URL in Chrome's full-screen mode?

Chrome does not allow that by default. See this bug report.

One option to achieve this would be to install MyAddressBar extension which will let you define a user configured key combination to bring up an address bar.

Chrome by default doesn't allow any type of UI in full screen mode. That is, without the use of an extension. [Reference Link]

However, if you using a keyboard with a Windows Key then you can push [Windows Key] + [R]. This will bring up the run box. Type in the address you want and hit enter. If Google Chrome is your default browser then it will bring up a new web page.

As an additional note, to switch between tabs, push [CTRL] + [#]. Replace the # with a real number.

You can use Vimium and access address bar with "o"/"O" hotkeys ("open URL"/"open URL in new tab").