Single Sign on without a visible login page

Is it possible to create a single sign on solution without the user having to manually enter their credentials on a login page?

Our current situation is as follows...

• We have a windows forms application that holds a username and password for a web application that we have developed (the end user is not aware of this username and password).
• The user can click a button in the windows forms application to launch the web site.
• This passes a payload containing their credentials
• The website calls a web service to authenticate the user

So we would like to now use single sign on, but the initial authentication must happen automatically (because the user does not know their credentials)

Is this possible?