(to) keep your chill is to not break down mentally, or to not lose your temper. If someone keeps their chill, they are able to endure moments of high stress.
Jane: Hey, do you know how Kate is doing? I heard she's had issues with depression and it's breaking her down.
Brad: Don't worry about her. Kate kept her chill. She had some troubles with the breakup, but she didn't break down.
Bob: Oh no! I did not study for the science test tomorrow! I am totally going to fail, and then I have to re-do this year!
Tim: Keep your chill. Someone posted a great summary on the school website, you should be able to learn for it in a day.
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