The northernmost borough of New York City is called the Bronx, with the definite article the. The borough is contiguous with Bronx County, which goes without the, but the official name of the borough (which is what matters, as the counties of New York City have no functioning governments) is the Borough of the Bronx. Bronx takes the definite article in most city documents (usually with the uncapitalized), and people native to the area usually use the article when speaking of the borough.
But as an adjective or as part of an adjectival phrase, Bronx usually goes without the—for example, a 25-year-old Bronx man.
The name comes from the Bronck family, whose Swedish patriarch Jonas Bronck came to the area in the early 1600s. The 500 acres they owned north of Manhattan came to be called Bronck’s land, and the river on which their land lay was called Bronck’s River. There are a few theories behind the definite article in the Bronx, the most plausible being that locals referred to the area as the Broncks’— as in, “We’re going to a party at the Broncks'”—and that this stuck.
As an adjective
A Bronx refugee who fled torture in his homeland proudly graduated Tuesday from a school that specializes in giving kids second chances. [New York Daily News]
The four-time nominated, Bronx-born percussionist’s career took off. [CBS New York]
Some diehard Edgar Allen Poe fans are helping to preserve the former Bronx home of the famed and mysterious poet. [NY1]
As a noun
But the owners of this castle in the Bronx sleep behind walls of fortified stone. [Wall Street Journal]
Teenagers in the Bronx are spending their summer running a farmers market in an effort to improve the health of residents in their community. [WFUV News]
Mr. Berg was born in the Bronx, but he is better known outside New York. [New York Times]