The Chekhov Gun is actually reference to a literary technique known as Chekhov's gun, whereby an element is introduced early in the story, but its significance does not become clear until later in the narrative. The concept is named after Russian playwright Anton Chekhov, who mentioned several variants of the concept in letters.
Sterling Archer presents Cyril Figgis with a Chekhov Gun while training him to be a ISIS field agent "Training Day." It is a Russian made, 25 caliber automatic pistol also referred to as an "underwear gun," due to Sterling's preferred hiding place for it. Though the name and Russian origin tends to suggest a Makarov or a Seecamp .25ACP, due to the close resemblance, according to the book How to Archer: The Ultimate Guide to Espionage and Style and Women and Also Cocktails Ever Written the Checkhov is a semi-automatic Walther TPH chambered in .22 LR.