One who has a prejudiced belief in the superiority of his or her own group. These days it's particularly applied to sexism, as in the well known expression "Male chauvinist pig!"
The word originally came from the name of Nicolas Chauvin of Rochefort, a possibly fictious soldier in Napoleon's army. He was supposedly wounded many times, and later given an poor pension of only 200 francs a year (plus a medal and a ceremonial saber). Even so, he remained fanatically devoted to Napoleon, always recalling the glories of Napoleon's rule.
He became famous when he appeared as a character in Charles and Jean Cogniard's play La Cocarde Tricolore in 1831. In this play, he was a patriotic young recruit; the same character later appeared in other french comedies, until his name finally became synonymous with excessive patriotism.
The more general sense, and then the very specific sense, in which the word is used today arose at some point in the 1970s, although the exact history of mutations is unclear.