If you're using a fix width for the chart then the only option I see to get the scroll bar is to select the "normal" layout for the element.
Another way to answer the problem is to build a dashboard for higher screen resolution. At the bottom left of the dashboard you can select different options and try different range that work for displaying all the columns the user could add. Obviously it works only if the end user have a higher screen resolution (which is always a good think to ask before building a dashboard for someone).
If you found another way, post it in the conversation I'd be interested to see how you did it.
That seemed to work well.
What I found is that it's really just a function of the resolution.
I can have the user just zoom in or out in their browser, and Tableau will resize it correctly. So the trick is that they just have to zoom out enough to see everything. That won't put the scroll bars in there, but at least they won't see the ##'s.