Chemical weapons were not used on the western or eastern fronts because Nazi Germany was aware that their use would lead to their enemies using them as well. The Wehrmacht was heavily dependent on horses for transport, and according to Hermann Göring [1] [2] (scans from Of Spies and Strategems), they could not devise a gas mask that horses were cooperative or effective with, making their logistical chain very susceptible to gas.

For two reasons:

1. Believe it or not, Hitler had an extreme aversion to the stuff after his experiences in World War I. The secret chemical weapons plant would be the only testing factory he made a point of never visiting.

That says a lot about his feelings on Jews.

2. In this vein, he feared retaliation with gas weapons.