I think that Chloe knows that Marinette is Ladybug, because she has her own kwami and she's seen Marinette's kwami before. Also, if you look back to the episode "Princess Fragrance", Marinette is chasing after Chloe saying: "Hey! That's mine!" Leading me to suspect that Chloe might've heard her say that, meaning that she knows Ladybug's true identity. Another theory is that in the Italian dub of "Queen Wasp", Chloe clearly says Marinette's name if you listen closely. That line was a mistake, though, and the Italian dubbers fixed it.

I know that this article is short, but that's just a theory. I understand that other people have mentioned the Queen Wasp episode, but I'm just pointing that out in case someone didn't know about that. Thank you for your understanding!