Single Page Application with No URL Change?

I am trying to build a choose-your-own-adventure-type website. I would like to use a single page application for speed and quality for full-page animations and videos. I need to know which, if any, single page applications would allow me to let a user click through a story path but not have a URL change. The background and words would change depending on the clicks, but everything else would remain the same. For example, a user will play the entire "game" but not see the URL change throughout their whole experience. I was wanting to use Ember, but it seems very URL dependent. Is there a single page application that would be best for a situation like this? Or am I barking up the wrong tree?