Up to Chrome V27 you could enumerate Chrome child window controls to get to the edit field and read the string value from there to get the current opened URL.
Unfort
AFAIK you could do this by creating a chrome extension which then communicates with the application using WebSockets.
There's even a Delphi implementation of the Web Socket protocol(with examples) -> DelphiWs
More relevant info here. That should get you started.
Chrome supports the Windows accessibility APIs, so you can use those to extract information both from the chrome - including the broswer bar - and also from web pages. Think of this API as a more abstract version of enumerating window controls.
Check out the Inspect Objects tool to explore what information you can get access to - it does look as though the address bar and contents are available.
You can get the same information in C# using the AutomationElement set of classes: