Your "no-chunk" would have a link to the login page, or the login form if you prefer. The "yes-chunk" would have a link to your resource, as well as a logout link. Or anything else you want the logged-in user to have.
As an example, on one site I use this as my Login resource's Menu Title
[[!Personalize? &yesChunk=`membersMenuTpl` &noChunk=`visitorsMenuTpl` &ph=`name`]]
The membersMenuTpl just says "Your Profile", while the vistiorsMenuTpl just says "Login". The URL is the same in either case; the page it links to handles what to do if the user is logged in or not with another Personalize snippet to either display the login form or the user's profile with a link to edit his profile as well as a logout link.
The point is that your Personalize chunks can contain anything you want. And of course you can always use the Login snippet's &loginResourceId property to send the user to whatever page you want on login.