Nope, Javascript interacts with web APIs that the browser has installed on it.
So in order to do this, there would have to be a way within one of the installed APIs to do this. Which I highly doubt there is. Also, Most browsers effectively run the DOM in a contained sandbox meaning that javascript and the web APIs can only access things from within its sandbox aka tab.
That said, it doesn't mean it's impossible. There may be an exploit in one of the API's allowing you to get other browsers info not usually available to you.
Feel free to crawl through all the web api docs to find an exploit and also try to engineer a way to break out of chromes tab sandboxing architecture via javascript.
I won't say it's impossible but it's highly unlikely unless someone makes a big mistake on a future release of chrome and one of the direct to browsers api's has an exploit. Sounds like a lottery win scenario to me just to read a tab.