http://en.wikipedia.org/wiki/Aaron_Burr
When it became clear that Jefferson would drop Burr from his ticket in the 1804 election, the Vice President ran for the governorship of New York instead. Burr lost the election largely due to a personal smear campaign orchestrated by his own party rivals, the Clintons of New York. Hamilton also opposed Burr, due to his belief (still controversial) that Burr had entertained a Federalist secession movement in New York. But Hamilton exceeded himself at one political dinner, where he expressed a "still more despicable opinion" of Burr. After a letter regarding the incident written by Dr. Charles D. Cooper circulated in a local newspaper, Burr sought an explanation from his erstwhile friend.
Hamilton had written so many letters, and made so many private tirades against Burr, that he could not reliably comment on Cooper's vaguely-worded statement. Burr demanded that Hamilton recant or deny everything he had ever said regarding Burr’s character, but Hamilton, having already been disgraced by the Maria Reynolds scandal, could not afford to make this gesture. Burr responded by challenging Hamilton to personal combat under the code duello, the formalized but largely antiquated rules of dueling. Both men had been involved in duels in the past, usually on the periphery, but Hamilton had particular qualms because his beloved son, Philip, had rashly entered into a fatal duel in 1802. Hamilton, who deplored dueling but nevertheless felt his honor was at stake, agreed to the challenge. The two would nevertheless use the same pistols owned by Hamilton's brother-in-law, which are now preserved by JPMorgan Chase & Co.
On July 11, 1804, the enemies met outside of Weehawken, New Jersey. When the duel began, Hamilton and Burr fired within seconds of one another. Hamilton's shot went astray, intentionally according to a letter he prepared before his death but Burr shot and fatally wounded Hamilton. The bullet entered Hamilton's abdomen above his right hip, piercing Hamilton's liver and spine, and he died the following day. Burr later learned that Hamilton intended to avert his fire during the duel. His response: "Contemptible, if true." Burr was later charged with murder in New York and New Jersey, but was never tried in either jurisdiction. He escaped to South Carolina, where his daughter lived with her family, but soon returned to Washington, D.C. to complete his term of service as Vice President. He presided over the Samuel Chase impeachment trial with the "impartiality of an angel and the rigor of a devil." Burr's heartfelt farewell speech in March 1805 moved some of his harshest critics in the Senate to tears.