I believe the answer is
g7 or g8.
The reason being
If White plays 1. a3, then Black plays 1... Kh7! and there follows
2. a4 Kh8
3. a5 Kh7
4. a6 Kh8
5. a7 Kh7
6. a8Q Kg7
and White is forced to stalemate in one of the other corners, as the Queen cannot move any closer than the e-file and Black will always have at least two squares to maneuver.
Meanwhile, if White plays 1. a4, then Black plays 1... Kh8! and there follows the same sequence as described above.
Maybe this is wrong, but I'd love to hear your thoughts.