It appears the first time that Arkham Asylum began showing up in the comic book stories was back in [B][I]Batman #258[/I][/B] (September-October 1974), though it wasn't quite the same as what we would later come to know.
[img]https://i67.servimg.com/u/f67/18/91/37/14/-_00a_13.jpg[/img]
And from [B][I]Who's Who: The Definitive Directory of the DC Universe Vol. I[/I][/B] (March 1985),
[img]https://i67.servimg.com/u/f67/18/91/37/14/arkham10.jpg[/img]