Monkeys are known for their chattering vocalizations and many species have long tails.
However, there are other animals that could fit this description depending on what you mean by "chatter":
* Squirrels: Some squirrels can chatter their teeth, and they have bushy tails.
* Rats: Rats can make chattering sounds and some species have long tails.
* Birds: Some birds, like parrots, can be quite chatty and have long tails.
If you can provide more details about the sound or the type of tail, I might be able to narrow it down further!