I don't chit chat during rolling or drilling. I don't like guys who do. Training time is for training.
But there is usually time before class, after class, in the parking lot, whatever, to at least talk a little with your training partners. It is a very good idea to take advantage of it to do so.
BJJ is an individual sport because you compete individually. But it's a team sport for training, which is most of the time. You simply cannot train by yourself. You need your training partners. They are your lifeblood.
It is very worthwhile to be aware of your training partners and treat them as people rather than realistic drilling dummies. After training, I will look around and see if anyone seems off or bummed out. If so, I'll go up to him and just say "Hey, what's up man? You okay?"
Most of the times, the answer is nothing. Maybe he had a hard day at work, maybe he's feeling a little sick, etc. Sometimes the answer is "I am thinking about killing myself." I got that answer once. I'm glad I asked. So was he. I think I was the only one who cared enough to ask.
Another example would be a training partner who is sitting out for a while with a serious injury. If he comes to the gym, you could just be totally selfish and ignore him. After all, he can't train, and you come to train, right? But if you do that, he will probably stop coming after a while. Then he'll restructure his life without the gym. When he heals, he won't come back. You've now lost a training partner.
A much better alternative is to take a little time to engage him as a person and make him feel welcome. Yes, that is going to take something a little different than a BJJ technique. You will have to use a social technique instead. But in return, your training partner will likely come back to help you with BJJ later on. Chances are he'll be an even better partner than he was before the injury.
It's important to realize that BJJ is not all about you. This is a very social art by definition. You can't just do kata all day or hit the bag to improve. You need others to make progress. If you completely refuse to socialize with others, you will hurt your own progress accordingly.