In Robert's Rules of Order who breaks a tie vote when the vote is within a chapter of several chapters?

There is no need to break a tie. When a motion is being voted on, it always requires either a majority vote, or a 2/3rds vote, to pass.

Thus if it is tied, that just means that the motion failed, for not getting the majority or 2/3rds it needed to pass.

So there is never any call to "break a tie".