How can I train her to leave the chickens alone? And at what point should I trust her alone with the goats?

The quickest way would be a shock collar. Or you could try a long lead , but odds are she wont chase them with it on, so you wont get a chance to correct her.
If she's been raised with goats, she should be OK with them now. I'd put her in with them and watch from a place where she cant see you.

Good luck

 

We used a shock collar for our anatolian for the same reason. She loved to "play" with the chickens. It worked after only having to zap her once or twice. After that, we would only have to use it every now and then to reinforce, but for the most part the behavior stopped.

 

We have a 6 month old Great Pyrenees LGD who has lived exclusively with our goats and sheep since she was 8 weeks old. She is in a playful adolescent stage right now and has been chasing 2 of my sheep (who run from her, giving her the reaction she is looking for) and giving the odd duck a run down to the pond, too.
Before using the shock collar (which will work amazingly!), we tied a small rope around her collar with a stick tied around the other end. Make the rope about a foot and a half long, so that it sits and gets tangled between their legs. We left it on C.C. the entire time she'd be outside. It stopped the behaviour immediately (because they can't run!), but, better yet, when it finally fell off her 3 days later, she hasn't repeated her bad behaviour once even!
Good luck!