It is, but only as part of the Dragonborn expansion pack. You can make Chitin armour for yourself, and also some Morag Tong assassins attack you, each wearing a Morag Tong variant of regular chitin armour.
Not on the regular game, if you really want to, get the game for PC. I'm sure they have a mod for it on the Skyrim Nexus or on Planet Elder Scrolls.
You can sneak in heavy armour too. The Heavy Chitin set weighs about the same as a Steel set, but offers more protection. You could imagine it's still handy for an assassin.
They are a criminal order of assassins, a split-off faction from the government sanctioned assassins guild, Morag Tong. They appear only when the Tribunal expansion is installed, and play a part in the beginning of the expansion's main quest.
TO join the Morag Tong, you must travel to the Arena Canton in Vivec. In the Canalworks there is a wooden door that leads to the Arena Storage. Inside you will find a number of crates, sacks and chests. As well as four rats and three wooden doors. The two doors on the left as you enter lead to dead end with some valuable items such as lockpicks and probes, while the door to the right leads to a room with a locked trapdoor. Pick the trapdoor and you will gain access to the Morag Tong secret guild hall.
Morag Bellingham was born in 1948.
Morag Bellingham was created in 1988.
Morag - moshav - was created in 1983.
Shlomo Morag was born in 1926.
Shlomo Morag died in 1999.
Morag Siller is 5' 2".
Morag Sims is 5' 1".
Katie Morag was created in 1984.