I think 'chat' is a little inappropriate.
The Japanese phrase ‘話を聞く’ refers to listening to someone's story (sometimes problem), so it is more important than a chat.
What theme is important depends on one’s subjective thoughts.
For example,
「どうしたの?何か嫌なことでもあった?話聞くよ?」
the situation: A girl looked sad and her friend tried to console her with listening what happened to her.
「ちょっとお話があるのですが」
the situation: Since he wanted to discuss the plan he had been in charge of, an office worker asked for his boss’s time.
これはアヤメに話を聞く重大なルールだ。
Since I don’t know the situation I can't explain it perfectly. But my expectation is that when the speaker ask Ayame some information, he or she has to follow the rule, like giving her equivalent information.
I thought of アヤメに話を聞く as asking her something, but I don’t know whether it is proper. If you give me the situation, I think I can tell you more correctly. :)