Use of the word "whilst".

Sometimes, I actually say “whilst.” As is my wont.

That link misattributes the quote to Homer, doesn’t it? I remember one of the female teachers saying it.

From the Season 7 episode Lisa the Iconoclast

I found “whilst” to be used fairly frequently (or at least noticibly) when I visitied Australia several years ago. I had assumed it was a Britishism, but thinking about it I realize that I don’t really recall the Brits that I know using it.

Anyway, for those of you that use it, when do you do so? In other words, what is the “gramatical justification” that j_sum suggests is there for its use?