Yeah, I guess it's "possible" in the sense that the position can be set up, but not legal. Still interesting.
Stalemate
Doesn't work, a SpieBoy. d8(N) or d8(B). My best is this position. I don't see anything blatantly illegal about it.

Well that position is indeed simpler than tonydal's, but just as illegal. But a simple tweak makes it look good.
Let's see:

grantchamp, that position is not a stalemate. If it were black to move, then it would be stalemate. As it is, white has a forced mate.

this is a wicked forum.
what is the fastest stalemate??
The fastest I have seen is ten moves. I don't know if it's possible to have one faster.

A stale stalemate:
A draw via three-fold repetition, but not a stalemate.
It's not the same?
Yes.

A stale stalemate:
A draw via three-fold repetition, but not a stalemate.
It's not the same?
A stalemate is a position in which the player to move has no legal moves. This is just one of five ways to get a draw in chess. The other four are mutual accord, threefold repetition, insufficient material (for both players, or for the player with time left if the other player runs out in a timed game), and the fifty move rule.
EDIT: And considering this, the fastest draw is simply draw by agreement before white's first move.
I'm fond of this particular position:
Either side to move is stalemate. It also allows for interesting positions like:
This is one I came up with. White to move is mate in one, black to move is mate in two. But what makes this unique is that all moves are forced for both sides--that is, white to move is mate in one whether white likes it or not, and vice-versa for black to move. My question is: is such a position possible where it is mate in one for both?