Practical, Immediate Dilemma

Does anyone have any advice about how best to transport a still rather wet oil painting by airplane?

Specs: I think I'm in a position to be able to claim whatever solutions are offered as carry-on luggage. The painting itself is comparatively thin, but made on Saturday. I'm flying it out tomorrow, Monday (if ever), and so I won't have a chance to run out and buy any esoteric ingredients.

Any advice?