What's the formal answer to a question beginning with "Shall we"?
Solution 1:
I think Yes, let's is a perfectly good answer here (that is, I don't believe it is any less "formal" than the use of the word "shall" by the questioner).
But, to avoid using that phrase, I think something like Absolutely would work (though it is a bit emphatic). You could also say That would be great or I would like that if the affirmative answer depends at all on your own opinion of the idea of chatting.