There are a few isolated instances where gas is said to have been used: in 1940, against some of the deeper Maginot line bunkers, a few cases in the Pacific... And then, in the context of WWII, phosphore would probably count as a chemical weapon, and was used during more than a few battles.
ORIGINAL: rader
EDIT: In summary, I think it was a mix of lack of effectiveness and fear of retaliation. I can't imagine that if it would have been a really effective weapon, someone wouldn't have started using it. But all sides were well prepared, kept stocks, and issued gas masks, etc.
I don't think the effectiveness of gas warfare was doubted. It had been used to good effect in WWI, to inderdict areas, force rotation of front line troops, prepare an area for assault (many contemporaries considered it more effective than barrage), and, most importantly, damage enemy morale (it truly was a terror weapon). I don't see how it could not have had the same effect on WWII armies, conscript-based like those of the previous world war.
It did have limitations: it could backfire and cause friendly casualties (but then, so does artillery...), fighting in environments where gas is present was very difficult (just try running, save fighting, with a gas mask), and area interdiction cut both ways. As such, it was not a war-winning weapon. But lack of effectiveness of a weapon has never prevented its use in war: think of infantry sabres in the napoleonic era, early types of amphibious vehicles, pistols, and (even recently) some models of submachine guns which jammed so easily while firing that they were (probably rightly) said to kill more friendlies than enemies (as any french reader who encountered the Mac49 would know, but I'm certain we're not the only one, esp. once reserves are concerned: pros get the good weapons, but world wars were fought by reserves, with the subpar stuff)
Besides, if it was thought ineffective, why would there be fear of retaliation?
My impression is that it was not used because it was considered a dangerous gamble. Gas could ruin enemy morale, but it could also ruin yours. The previous world war had seen quite a few mutinies from front line troops, support for the war sometimes wavered. This made the use of gas a risk.
Francois