I don't want to be rude. But I don't want to chat with this person in Gmail. Will he/she be notified or otherwise know if I say no to his/her chat request?
No, they will not receive any notification about your action. The user will continue to see you in their list with the "Invited" status.
S/he sent you a chat invitation. Whether you press "No" or leave it alone, whether s/he gets a notification or not, either way s/he don't get to chat to you. So, the end result is same.
No, s/he wont get any notification.
P.S. - BTW, if that person doesn't get a notification, that's even more rude, that means you are ignoring him/her.