IIRC, in 1992 there was a three way Democratic Primary between Alan Dixon, Albert Hofeld, and Carol Moseley Braun. Hofeld was a multi-millionare who self financed his campaign--a campaign that consisted of a long line of TV adds that pummelled Dixon and left Moseley Braun untouched. Mosely Braun did pretty well in the televised debates, stayed above the Hofeld-Dixon fray and rode the three way split of the vote (winning in 7 out of 102 counties) to victory.
In retrospect, having voted for her back in that primary--it is one that I regret. She was a poor Senator, (personal scandal sank her reelection bid in 1998) and a completely unhinged candidate for mayor of Chicago last year.
Ill_Ind
So basically it was the Dem's version of this years Nebraska Republican Primary with a woman winning while the 2 male candidates took pot shots out at each other.
I think Mosely-Braun would be mayor of Chicago right now if Rahm didn't run though.