oh, thank you Wikipedia

"The Bronx" is the only borough in New York City that, in its capacity as a borough, is referred to, in both law and popular usage, with the definite article ("The"). (The name of the coterminous "Bronx County," however, does not include a "the.") The best explanation for the definite article is that the original name of the borough, when it was annexed from Westchester, was "The Borough of the Bronx River," referring to the river that passed through the borough.