The good news: Two models of Asus Eee, the 1101HA and 1005HA, are eligible for free upgrades to Windows 7. The bad news: Your 1101HA needs to be preloaded with Vista Home Premium and your 1005HA needs to be preloaded with Windows XP Pro or Vista Business.
As Lilliputing so eloquently put it, "I didn't even know those options were available". If you own any other type of Asus system, check the link to see the company's other Windows 7 upgrade offers. [Asus via Softpedia via Lilliputing]