Just taking this from Fookiepedia but it would seem that Vader taught Chewie in ancient noble art of Teräs Käsi back when he was still Anakin Skywalker.
HERE ARE THE FACTS.
Already Anakin had begun to see the Jedi order as an unjust organisation and took it upon himself to pass on Jedi skillz under the guise of a member of a martial arts society, the Followers of Palawa.
This was a total bogus and made up organisation apparently obsessed with volcanoes and sailing but the moves were all adaptations of genuine Jedi martial art techniques with a few random attempts at disco that Anakin was really into at the time.
THIS IS WHERE THE FUN BEGINS.
He went by the pseudonym of Master Chop-Chop Miyagi and trained pupils or Onyenz as they were called from all over the galaxy from his Sandes Dojo on the planet Bunduki .
Many of the techniques and attacks of Teräs Käsi were named after various things his pupils noticed their Master doing in private. These include :
1. The “Disco Point”
The most basic of all Disco moves, this defensive stance communicates strength to your opponent.
2. The “I’m Watching You”
The basic Disco Point also serves an offensive purpose as an aid in surveillance.
3. The “Bunny Slope”
As a rule, Disco fighting requires a sturdy base. The “Bunny Slope” bounce (because it may make you resemble a dorky beginner skier) forms the basis of many Disco moves.
4. The “The Russians Are Coming”
Modified from a Russian (Russia is a planet in the eighth universe) folk dance, this advanced maneuver allows you to travel quickly towards your opponent while also looking Psychlo-esque.
5. The “Stealth Walk”
Excellent for creeping up on bad guys.
6. The Giddy-Down
This clever action is meant to trick your opponent; while he thinks you’re about to move, you in fact stay in the same place, upper body completely static. Advanced: Maintaining an intense, Blue Steel-like stare into your attacker’s eyes.
Attack Moves
7. The “Groovy One-Two”
An effective way to strike your aggressor. Note the correct positioning of the hands, extending palms first (not fist), so you can protect your knuckles.
8. The “Yoda in a Skoda”
This moving kick allows you to stay close to the ground.
9. The “Wheee!!!”
Inspired by wrestling techniques, this jump will squash your opponent while also confusing them by your incongruously jovial disposition.
10. The “Butt Jump”
A variation of #9, you may imagine a rug being pulled out from under you. And under that rug is a bad guy. Who just got passively whooped by your butt.
11. The “Grover Strike”
An adorable and easy technique for the un-coordinated.
12. The “Wax On, Wax Off”
To master this advanced move, you must first wax Master Miyagi’s skyhopper several times.
13. The “Diva Dance Instructor”
Essential to proper execution of this action includes a shiny tank top and diva mentality. Extend one arm while spinning, effectively slapping your opponent. With pizzazz.
14. The “Jolly Jaywalker”
This move is about concept: Imagine you are happily walking down the street, and doing it in the most groovy manner possible. You are likely to hit someone.
Intimidation Tactics
15. The “Needs No Introduction”
Disco Fighting is also an intellectual form of combat, so one’s entrance is everything. This step requires you to produce a lit deathstick out of nowhere, and to act as if that is totally normal.
16. The “Man Of A Thousand Balls”
This jazzy reveal communicates power and influence. It also has the potential to blind your opponent right off the bat.
17. The “Face Wave”
During breaks or before attacking, this “whatcha gonna do?” move distracts your partner and also makes them feel bad that they are not as cool as you.
18. The “Sad Split”
This move is meant to look as though it hurts, showing your opponent that you feel no pain.
19. The “Scared Shitless”
Many use this knee-wobbling tactic to communicate sarcasm — “Oooh, I’m so scared.” Keep in mind that this controversial move has been known to backfire given the perilous and violent nature of Teräs Käsi; members of the Sandes Dojo are often actually scared shitless.
Chewie was considered Anakin's seventeenth best student
Not wishing to extinguish the flame of Disco from the galaxy Vader spared his former pupil.