In Chrome, use the keyboard cmd+shift+f to go in to full screen mode.
Use it again to exit full screen.
To fill in the Window (not the screen) I recommend the Chrome Extension called "iZoom", found here
https://chrome.google.com/webstore/detail/izoom/iheccogfcpjfjbnlohnlgdljaefpgaoi?hl=en-US
Automatically changes zoom level to fit window width. With three different zooming modes.