They did.

The German army was the most prolific user of gases (phosgene, mustard gas, chlorine...there were several in use) but the British Empire as a whole, the French, the Americans, and pretty much every combatant on either side tried it at least once. The first British attempt was at the Battle of Loos in late 1915. The first French attempt (made with non-lethal tear gas) was even earlier, in August 1914 barely a month after the conflict broke out.

Looking at these early attempts tells us why it wasn’t more widespread. Even for the most enthusiastic users, gas was a fairly specialised weapon, useful primarily for the fear it engendered in the enemy. British figures kept from 1916 until the end of the war show that some 70% of gas casualties would be cleared for duty at the front again in six weeks, and almost all of them within three months, but gas terrified soldiers.

Fear is a plus, but gas as an effective offensive weapon was actually really difficult to use. Combatants would have to wait for a day when conditions were right - the wind must be blowing in the right direction, blowing neither too strong nor too weak, the sun could not be too bright...and because most of the gases in use were water soluble, high humidity was helpful but it could not actually be raining - so depending on the time of year it could be quite frustrating trying to wait for that day. In the first British attempt at Loos, most of the gas that was released blew back in the faces of the men who had released it, and it took some further experimentation to perfect gas shells that could work from greater range. Even if they got the gas over towards the enemy, the combatants that had released it often had to risk it later hurting their own men too; chlorine gas is several times heavier than air, which means it collects in low-lying areas like the base of trenches rather than dispersing. Mustard gas behaves similarly. If you clear a trench with gas, the gas will still be there when your own men advance to capture it. If they lack effective protection (which many troops did until the later stages of the war...as it so often does, the weapon progressed faster than defences against it) then your own troops are going to take casualties from the gassing too. You’re going to have to have a plan to deal with these wounded men.

Source:

The Imperial War Museum in the UK has some excellent first hand accounts.

The US Army Command and General Staff College also has an interesting paper.