Question: Obviously, Han understands Chewbacca (almost) perfectly. In the prequel trilogy, Yoda seems to understand him too. In at least one scene in the original trilogy, C-3PO also understands Chewie, which is logical, since - as a protocol droid - translation is one of 3PO's primary functions.

> 
> THREEPIO: Captain Solo, this time you have 
>  gone too far. 
> 
> 
> (Chewie growls) 
> 
> 
> THREEPIO: No, I will not be quiet, Chewbacca. 
>  Why doesn't anyone listen to me?
> 
> 
> 

Does anyone else in the *Star Wars* movies understand Chewbacca?
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Answer: 
**Understand Shyriiwook, Master Yoda does**
-------------------------------------------

> 
> When he told them the problem, **the Wookiees nodded and barked at each
> other so fast that it was difficult even for him to follow the
> conversation.** Then they turned and offered him one of their escape
> pods. Yoda accepted at once. The only problem left was how to get past
> the clone troops to the pod.
> 
> 
> [Revenge of the Sith - Official Novelisation](http://starwars.wikia.com/wiki/Star_Wars_Episode_III:_Revenge_of_the_Sith_(novel))
> 
> 
> 

As does Leia (although not as well as her official profile suggests)
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> 
> *“According to her diplomatic profile, Princess Leia speaks both
> Huttese and Shyriiwook fluently. **Regretfully, and as Your Majesty is
> keenly aware, the princess is merely proficient in Shyriiwook.** This
> is, naturally, a failure of mine and not the princess, but I worry
> that such an error might cause her embarrassment. Oh, it is too, too
> humiliating.”*
> 
> 
> [From a Certain Point of View](http://starwars.wikia.com/wiki/From_a_Certain_Point_of_View) - [Eclipse](http://starwars.wikia.com/wiki/Eclipse_(short_story))
> 
> 
> 

---

Lower canon films
-----------------

If we also include the [Star Wars Holiday Special](http://starwars.wikia.com/wiki/The_Star_Wars_Holiday_Special), then we can also add

**Chewie's wife Malla**, **his son Lumpy** and **his father Itchy** as well as **human trader [Saun Dann](http://starwars.wikia.com/wiki/Saun_Dann)**, all of whom demonstrate an ability to understand Chewbacca.
*Note: I don't like getting rep from self-answers, so this is a Community Wiki answer.*

Legends:
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One of the other main characters from episodes V and VI, Lando Calrissian, speaks Shyriiwook well enough to bicker with C-3PO over a translation:

> 
> Chewie said something. Nobody spoke for a moment. Leia said, “Well, is somebody going to tell me what he said?” 
> 
> 
> Threepio got it out first: “Chewbacca says the woman made him very nervous.” 
> 
> 
> “He didn’t say ‘very,’” Lando said. “Just plain ‘nervous.’ ” 
> 
> 
> “Excuse me,” Threepio said. “I inferred the modifier from his tone. Wookieespeak allows for such shadings.” 
> 
> 
> “You saying my Wookieespeak is bad?” Lando said.  
> 
>  - *Star Wars: Shadows of the Empire* 
> 
> 
> 

Throughout this book, Lando shows his proficiency in understanding Shyriiwook on a regular basis.