You may want to describe what you mean by fullscreen, because the stuff I see tells me you're already looking at the AE user interface full screen. What you see is what you get. You get to pick the layout and the panels you see
So if you can enlighten us as to what you mean by the term "chrome" in better detail, it might be helpful. As might the reason why you think it's so important to get rid of it... other than you think it's offensive-looking, of course.
I believe by "chrome" he means the light-grey part of the window that runs along the top of the After Effects window, and contains the red yellow and green buttons to manage the windows.
This bit of the interface is disposed of in Photoshop by tapping the F key which cycles you through a couple "true full-screen" modes.
To my knowledge, there is no equivalent option in After Effects, and you're stuck with a few pixels of extra space at the top.