Check out: http://thenextweb.com/
If you look at the "All channels" column on the left, you can see that this container is in fact scrollable. The scrollbar will only appear when the container is hovered over. This is a good way to show that the container is scrollable, but keeps the design clean when no hover is occurring.
If you are worried about the usability of a thin scroll bar, what you can do is increase the width of the clickable area. See the highlight green area below:
You can see that, even though the scroll bar is quite thin, you can expand the clickable area (green area) so that visually the scroll bar appears thin, but there is in fact a wide area to click and drag in.
Make sure you also allow users to use their mouse wheel if they prefer, as some people may prefer not to use scroll bars. One thing to note on the example site (http://thenextweb.com/), it has very slow scrolling within the container. I would try and match it to the speed of the browser window.