Chatter (even though I haven't tested with/played against it yet outside of my Boomburst spam team) doesn't appear to be that bad. Pidgeot-Mega seems good with it, but everyone else who can't abuse Boomburst and/or doesn't mega-evolve just falls short. You're stuck with 3 terrible abilities (Big Pecks, Tangled Feet, and Keen Eye) as your options. In Balanced Hackmons, anyone can run chatter (Rayqquaza) with virtually 0 cost, but here it's not the case. You're also gifted with not the best coverage (Boomburst, Chatter, Heat Wave, and a Hidden Power of your choice), meaning things like Flash Fire steels (especially the omnipresent Doublade) can and will deal with you. Yes, you get Nasty Plot, which is definitely a boon, but stuff like Chansey can come in and copy that, turning the strat against you.
If push comes to shove and you want to deal with Chatter reliably, there are some Soundproof users to inherit from, such as Exploud, which also gets Boomburst as well as much better coverage, and Bouffalant, which gets SD, Edgequake, and still more Physical coverage. You could even inherit from da mimez if you want to, as it actually has a good physical movepool (as well as Baton Pass, Healing Wish, and a better special movepool than Chatot). Shield Dust is terrible, don't run Shield Dust. Additionally, Chansey is still a thing, and as we're all aware Chansey is the special wall of choice for everyone on the face of the earth. If you wanted to be sort of niche you could run Own Tempo, but it's probably not as good as Soundproof unless you inherit from Smeargle.
Overall, as it stands now, I haven't really seen evidence that Chatter is that broken. I don't have enough of an opinion on this to give a truly final result as of yet, but it doesn't seem broken now.