It's a very important part of Russian folk lore - a so called "Hut on Chicken Legs", or "Chicken-Legged Hut" ("избушка на курьих ножках"). There are no stories featuring it as a main character, it's just a house where Baba Yaga lives, and it appears in every fairy tale about Baba Yaga. In some tales these huts are semi-intelligent creatures, but mostly it's just what you can call a "smart house", albeit with an attitude.

An integral part of every tale about Baba Yaga vs. some kind of hero is a chant, which is needed to be said before you can enter the Hut on chicken legs when Baba Yaga is absent: "Избушка-избушка, повернись к лесу задом, ко мне передом" (Hut-hut, turn your back to the forest, your front to me). After this a hut makes a turn and reveals a door which was hidden and/or unavailable before then.

Some theories on the origin of such an exotic dwelling are mentioned in the article about Baba Yaga: Wiki.

Due to its familiarity (everyone knows about this hut since childhood) its images are often used in cartoons, jokes, etc.:


A sand sculpture of (a little unconventional) Chicken-Legged Hut in Kharkov (Ukraine):