What OS, browser, and web server are you dealing with? (Or do you have to support more than one combo of those?)
There might be some server-specific or browser-specific solution. For example, I think that for IIS if you disable anonymous access and enable integrated authentication, then IE will just send the user's credentials along, without ever prompting for a username/password. I think there's also a mod_auth_something for apache that can be configured to work the same way, checking Active Directory for its data.