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.