DBA From The Cold (9/16/2014)
What I would do is grant the user SELECT on the sys.server_principals table in the master database. This will allow the user to see all the logins.
This is not quite right. sys.server_principals is not a table, it is a catalog view to which everybody already has select permission on. By default you are only able to see your own login, system logins, and fixed server roles.
you could either grant ALTER ANY LOGIN which in this case is excessive, or you can grant view definition on all logins to the login you want to have access.
GRANT VIEW DEFINITION ON LOGIN::[loginname] TO [viewing_loginname]