Sorry, missed the priorities in your original post.
Perhaps a short-cut in this case but if you're happy the carbon bearing the chlorine is S my thoughts were that for the purposes of this,
* the chlorine is identical in priority to how the hydroxyl sits on the other chiral centre
* if the compound was meso it would be R,S
* so it's S,S
You could also look at it as the highest priority group is at the back, which reverses any assignment.
Or alternatively don't forget the hydrogen (on the carbinol) is coming out of the plane so just rotate the molecule around the C-C bond that contains the two chiral centres