There are two ways (at least). Section access is one way. That's probably the better option, but maybe a bit more work to set up. See here for an introduction pdf.
Or you can use the OSuser() function in the conditional expression of the dimension.
if(OSUser() = 'MyDomain\MyUser',1,0) will show the dimension only if the user is named MyUser and part of MyDomain.
Thanks, Gysbert. It works. But the requirement has somewhat changed for me.
Now I want to restrict not by MyUser but by MyDomain. So let's say that anyone who has the domain "MyDomain" should be able to see it and anyone who does not should not be able to see it. It should no longer be driven by username but by domain name.