Historical question. Why didn't we use chemical weapons during the assault on Okinawa?

Its a lazy Sunday afternoon and I'm watching a documentary on the planned invasion of Japan.  They're doing a great job of giving the tick-tock of the decision making but I'm baffled.

In the discussion of the invasion of Japan by the Joint Chiefs, they're saying that chemical weapons were proposed for use against the Japanese civilians but that the Army Chief decided that incendiary bombs were more effective because they gave the added benefit of incredible property destruction.  He did however think that chemical weapons might have a place during the landings if they ran into pockets of resistance.

The rivalry between the Army and Navy raged with the Army pushing hard for an invasion and the Navy pushing a blockade/bombardment strategy.

Then Okinawa happens.

US Marines are faced with an island fortress and some of the most formidable defenses known to man.  The number of Marines killed and injured would be unthinkable today.

Which leads me to my question.  Why didn't we use chemical weapons on Okinawa?  Don't get me wrong.  I know how horrible they are but this was full on combat and the times were much less squeamish than we are today.  Additionally we had no problem in firebombing Tokyo or using atomic weapons later.

So why the prohibition on chemical weapons.