"Western military chiefs have expressed concern that Russia could resort to the use of chemical weapons in Ukraine," according to a UK Parliament research briefing published on March 18, 2022. The report provides relevant historical context:

During the Cold War, the Soviet Union had the world’s largest stockpile of chemical weapons: with the Organisation for the Prohibition of Chemical Weapons confirming it held almost 40,000 metric tons of chemical agents, including VX nerve gas, sarin, soman, mustard gas and phosgene.

Despite agreeing to destroy its stock of chemical and biological weapons by April 29, 2012 in accordance with the Chemical Weapons Convention, Russia has used chemical weapons in targeted attacks as recently as 2018 and 2020.

As Matthew Bunn, Professor of the Practice of Energy, National Security, and Foreign Policy at Harvard Kennedy School, explains:

They have used small amounts of chemical weapons in assassinations or assassination attempts against dissidents, both in Russia, against Alexey Navalny, and in the U.K., against Sergei and Yulia Skripal. [...] Under the Chemical Weapons Convention, they’re not supposed to have any chemical weapons anymore, but are believed to have significant stocks.

Western governments are preparing for the possibility of Russian use of chemical weapons. On March 23, 2022, the New York Times reported:

The White House has quietly assembled a team of national security officials to sketch out scenarios of how the United States and its allies should respond if President Vladimir V. Putin of Russia — frustrated by his lack of progress in Ukraine or determined to warn Western nations against intervening in the war — unleashes his stockpiles of chemical, biological or nuclear weapons.

UK Prime Minister Boris Johnson has warned Russia against the use of these weapons, as reported by the Guardian on March 24, 2022:

Boris Johnson has warned of “catastrophic” consequences for Russia should Vladimir Putin use chemical weapons in Ukraine, though stopped short of saying that would include a military escalation.

Will Russia use chemical weapons in Ukraine in 2022?

This question will resolve positively if, between March 1, 2022 and January 1, 2023, any of the following three conditions are met:

• The heads of state of at least two permanent members of the UN Security Council make a definitive statement to the effect that Russia has used chemical weapons.
• There is a resolution by the UNSC or by the UN General Assembly condemning the use of chemical weapons in the Ukraine by Russia.
• At least 6 of the following sources make a definitive statement that Russia has used chemical weapons: The Economist, The New York Times, Reuters, The Associated Press, The Guardian, The BBC, Al Jazeera, South China Morning Post, The Financial Times, The Washington Post.

Clarification on March 29, 2022: please note the following definition includes the use of chemical weapons in targeted attacks, including poisonings.

We will use the definition of "Chemical Weapons" provided by the Organization for the Prohibition of Chemical Weapons, whose mission is to implement the provisions of the Chemical Weapons Convention:

“Chemical Weapons” means the following, together or separately:

a) Toxic chemicals and their precursors, except where intended for purposes not prohibited under this Convention, as long as the types and quantities are consistent with such purposes; b) Munitions and devices, specifically designed to cause death or other harm through the toxic properties of those toxic chemicals specified in subparagraph (a), which would be released as a result of the employment of such munitions and devices; c) Any equipment specifically designed for use directly in connection with the employment of munitions and devices specified in subparagraph (b).

Where:

“Toxic Chemical” means:

Any chemical which through its chemical action on life processes can cause death, temporary incapacitation or permanent harm to humans or animals. This includes all such chemicals, regardless of their origin or of their method of production, and regardless of whether they are produced in facilities, in munitions or elsewhere. (For the purpose of implementing this Convention, toxic chemicals which have been identified for the application of verification measures are listed in Schedules contained in the Annex on Chemicals.)