Auto workers at Volkswagen AG’s Chattanooga, Tennessee plant voted against joining the United Auto Workers Friday night, handing the labor union a bitter defeat in a hard-fought effort to organize workers at a foreign-owned auto plant in a southern state.

In three days of balloting that ended Friday, 833 hourly workers voted against UAW representation, while 776 voted in favor, with 93% of eligible employees voting, according to preliminary results released by Volkswagen. The result isn’t official until the...