How to add Campaign Source on Web-to-Lead form?

How to add Campaign Source on Web-to-Lead form?

We are planning some advertising campaigns on several different Web sites. We can use the Lead Source field to capture certain information, and we have added several custom fields to our Leads. But I just realized that Campaign Source is not available as one of the fields we can select when using the Web-to-Lead form generator.

In fact, while trying to figure this out I also noticed that Campaign Source is not listed on the Lead Settings/Fields List page. But it is shown on the Lead Settings/Edit Page Layout. And it's obviously listed on the New Lead page.

So, how can I get the Campaign Source into the Web-to-Lead form? Is this a bug in the We-to-Lead form generator? Can I add it manually as a hidden field after generating the form?

Please tell me this is possible somehow - I am so close to having a perfect system configured for my customer.