How can I add a property to the window object in Chrome using Applescript?
I discovered a workaround. Might not be the best, but the following line executes the JavaScript I have in mind while also setting properties of window:

tell front window of application "Google Chrome"
    set URL of active tab to "javascript:" &amp; window.myVar = "myValue"
end tell


Using this, myVar properly returns "myValue". Nice.