Yes - probably - but not in large quantities. The war in Tambov was especially brutal even by the standards of the Russian Civil War. Often quoted is the order by Tukhavchevsky and Antonov-Ovseyenko that:

"The forests where the bandits are hiding are to be cleared by the use of poison gas. This must be carefully calculated, so that the layer of gas penetrates the forests and kills everyone hiding there."

However the actual use of gas weapons seems to have been slim. According to articles by Alexander Bobkov and Pavel Aptekar, only about 2,000 gas shells were delivered to the Red Army in Tambov and only 320 fired. Whether they were lethal chlorine gas or non-lethal tear gas (or some other type) is not known.

Gas then does not seem to have been of much importance, except in anti-communist propaganda which was keen to emphasize the brutality of the Red Army. In any case the Blue Army in Tambov was put down by conventional means. Red Army detachments shot hostages and burnt villages, eventually annihilating the partisans with no quarter. The peasant rebels for their part showed no mercy, even crucifying captured Red Army soldiers to trees with railroad spikes. Gas was not the worst aspect of the Tambov battles by any means.

Sources:

Pavel Aptekar, "Khimchistka po-Tambovskii"

Bruno Cabanes, The Great War and the Origins of Humanitarianism

Seth Singleton, "The Tambov Revolt 1920-1921"

Jonathon Smele, The "Russian" Civil Wars 1916-1926

Edit: If you are interested in the Tambov rebellion, there is a good fictional treatment in Alexander Solzhenitsyn's book of short stories, Apricot Jam.