In an interview posted two days ago, American McGee talked about the original Alice game being offered as DLC to fans that purchased Alice: Madness Returns on consoles. EA has officially confirmed this and provided additional details. If you buy Alice: Madness Returns on the Xbox 360 or Playstation 3, you will get a download code which will allow you to play the original American McGee's Alice for free.
If you don't want to pick up the sequel, you can spend $10 to buy the game over Xbox Live or the Playstation Network. Unfortunately, this deal is not being extended to those who purchase the Alice sequel on PC. Alice: Madness Returns will be available on June 14th.