Sure. Basically it'd just be a one-way chat application, where the sender is always the same. The client side could be implemented as an Active X control, or, better yet, a Java applet, and embedded in a web page. The server side could be implemented using any suitable language.
Or, if the news can wait until the next time the user loads a page, you could just show the last X# of news items in a part of the page. This would be easier to implement, as it can be done with any suitable server side language, and it doesn't depend on the client side supporting plugins.