a3
If black tries Qxe3, it's stalemate.
If after a3 white tries to take the a3 pawn, black can mate via Qg2 or Qh2. If white tries to check by moving to the first rank, Qf1+ forces a trade of queens and leads to the eventual queening of the a-file pawn.

Pg5 and white aufgegeben.- Mare or D change.- After PT promote.-

Sorry: mare is a mistake.- mate is correct.-

Though I came up with the answer on my own, I have since run the position with a couple of chess engines to see if crackingchessmen's answer led to mate faster. His seemed like a pretty good answer to me.
According to the two engines (Fritz 5.32 and Crafty 19.9), a3 leads to mate in 8 or 9. Strangely, the two engines differ in how many moves will lead to mate. I haven't compared the two outputs yet to see where the moves differ.
On the other hand, g5 does not show up as leading to a forced mate.

I realize chess engines are not infallible, so I'd be interested in hearing other views.

Dear Mr. djpnola: ¿What play you after g5? I only saw two or three moves ahead.- My show is not based in a forced mate but in conceptual thoght.- I am only a man.- Sincerely your, Cr.
Oh. my english... is...

Dear Mr. djpnola:Yes sir.- My analisis is wrong.- If g5 , QC1+ and draw.- Congratulations.- Crac...Crac...Crac...

I AGREE WITH djpnola: a3 is the winning move.

Yes, the simple a3 is the winning move. White can do nothing better than exchanging the Queens; he cannot leave the a7-g1 diagonal without check.

But OTB, I probably would have played g5. This move is SO seductive, once you have discovered it! Doesn't it seem to be a really "brilliant" move? Leaving the White Queen alone, but threatening mate in one? However, after Qc1+ Qf1+ QxQ KxQ hxg5 Black is missing a deciding tempo: BOTH pawn are promoted to Queens, resulting in a probable draw.

For me, this position teaches me (once again) not to try spectacular moves if you can win with simple moves - especially when under time pressure.

I also saw the seductiveness of g5! I agree with djpnola on a3.

I ran into an interesting problem though. At first, I was reading the board completely wrong, thinking that Black's Queen was under attack by the g3 pawn. I kept seeing that if Black took the White queen, it was a draw, and other moves were trouble for Black. Did anyone else hallucinate like this? Or just me? :)

If ... QxQ
Kg4... .- Black win.-
Crac...Crac...

Yes, Heather, I had the board reversed too, and more than once. I'd get the board right in my head and then I'd forget and see it the other way (that white was moving DOWN the board and black was moving UP).
It's like those trick pictures where first you see one thing and then the other and they keep flipping in your eyes' mind.

Interesting, though, that even if you read the board wrong (white moving DOWN the board), it's still a draw if QXQ.
I wonder how many times that kind of situation comes up in a position.

A chess palindrome, maybe?