You could just make it into a TextBox that's Read Only which just looks like a TextBlock, kind of like;
The ScrollViewer ContentElement would be in a TextBox by default, you could substitute for a ContentPresenter instead if you like also.
Then put it into effect;
Hope this helps!
ADDENDUM: As @doodleus pointed out in the comments. Template binding the Content Property within the template may be necessary. As "ContentElement" is a named part of the Silverlight TextBox control. One of the little nuance differences to watch for in the different xaml Variants. I must not have paid attention to the Tags when I originally created the example. So kudos to him for correcting me.