In the event a tie should occur in the senate, the constitution provides who shall be the tie breaker?

The Vice-President of the United States.

The language in the Constitution (Article I, section 3) is as follows:  "The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided."

Current Vice-President Mike Pence has served as the tie-breaking vote on a number of occasions in a Senate that is deeply divided along partisan lines.  As of the end of February, 2018, Pence had cast a tie-breaking Senate vote nine times.