There are a number of characteristics attributed to chivalric behavior found in Sir Gawain and the Green Knight.

A knight was to adhere to certain rules. Wikipedia.com notes that these included:

...[d]uties to countrymen and fellow Christians: this contains virtues such as mercy, courage, valor, fairness, protection of the weak and the poor, and in the servant-hood of the knight to his lord.

Mitchell's website on chivalry provides more specific details:

Honor:

Always keep one's word

Always maintain one's principles

Never betray a confidence or comrade

...and...

Courtesy:

Exhibit manners

Practice the rules of decorum

Be respectful of host, authority and women

When Gawain travels to meet the Green Knight, in answer to his original challenge issued the year before in Arthur's court, the young knight shows his honor in keeping his word to show up, even though he believes that when he faces the mystical Green Knight, he will surely die.

When Gawain arrives early, near the chapel—the appointed meeting place—he is invited to spend the holidays with Bertilak and his wife at Bertilak's nearby castle. Unknown to Gawain, Bertilak is actually the Green Knight, who tests Gawain each day to know if he is a true and honorable knight. The tests come at the hands of the wife of Gawain's host, as she does her best to woo him with kisses, romantic advances, and gifts.

Gawain adheres to the rules of courtesy, never giving in to the wife's overtures. Gawain, fearing for his life, however, does not divulge to his host the gift of a magic belt, given by Bertilak's wife, to protect him from death in his upcoming confrontation with the Green Knight. This is a betrayal of his code of honor, but when the Green Knight and Gawain finally meet, Bertilak exposes his real identity, revealing his knowledge that his wife gave Gawain the Green Knight's magic belt.

'That belt you're wearing: it's mine, my wife /

Gave it to you—I know it all knight...

...But you failed a little, lost good faith...

...For love of your life. I can hardly blame you.' *

Bertilak forgives Gawain for wanting to save his own life, noting that in all other ways, the young knight did his best to be faithful to the chivalric vows he had pledged in becoming King Arthur's man.

'You stand confessed so clean, you took /

Such plain penance at the point of my ax, /

That I hold you cleansed, as pure in heart /

As if rom your birth to this day you'd never'

Sinned.' *

In Gawain's second meeting with the Green Knight (in the person of Bertilak), we see how the young knight does his best to adhere to two of the characteristics of chivalry: honor and courtesy.

*Translation by Burton Raffel; printed in Adventures in English Literature. Orlando: Harcourt Brace Jovanovich, Publishers: 1985.