Ctrl+Shift+I or F12 -> Elements, It should show your source. Right click on any element and click
Edit as HTML
There are some extensions that look like what you want: https://chrome.google.com/extensions/search?itemlang=&q=editor
Live WebSite Editor look promising.
Added by barlop
I see that (after ctrl-shift-I / F12), right clicking the
<HTML..> or </HTML> tag and clicking "edit as html". allows me to edit anywhere within it. Choosing the opening tag means the popup for editing just covers all the html source that's there - which is very neat in terms of space when editing. Choosing the closing tag might be useful as the popup then appears under the html so you see a before/after. Or better, as benjamin says, F2 to edit, ctrl-enter to commit.