She lost in 2002, President Bush was in office. You're thinking of Carol Moseley Braun, who was elected Senator from Illinois, IIRC, in 1992 (year of the woman - barf). She lost her re-election bid in 1998, and Clinton appointed her as an ambassador, I forget to where.
Fiji.
"You can't get any further away before you start coming back." -- The Truman Show