You'd be doing this with the big site's permission, right?
Then yes, as Chris said use a canonical pointing to the original source. That content on your site won't be indexed, but it will be there for visitors to your site to read without leaving your site, which is why I am assuming you'd do this in the first place.
And to make a quick point about the dreaded "duplicate content penalty"--it's not a penalty as such--Google just makes a call on which version to index and which one to drop. In this case, the original would probably indexed with or without the canonical (though you should use it anyway).
That being said, if you have a lot of scraped content, Google may not consider yours to be a quality site and that creates problems.