There is indeed a fair amount of information about "the Matriarch" in WoD: Chicago. I won't quote all of it, but perhaps I can hit some of the important points:
- Her name is Jaqueline Edens, and you are right that she is a Carthian.
- She was the child of an elite family of bankers and politicians.
- She ruled with an egalitarian politic from 1969-1986 (the shortest stint of any Chicago Prince).
- Her rule was one of freedom and respect for the responsibility of common kindred, but pretty much only the Carthians were happy with it. When she was deposed in 1986, she had opponents at every angle who felt that more top-down control was necessary.
- Edens was partially brought down from the inside by her "chief information-gatherer," Norris Kleinspiegel, who was secretly working for Maxwell in spite of the broad power Edens had bestowed on him.
- She disappeared after the coup and there is no definitive word on her whereabouts. She is probably hiding out in the Undercity in torpor.
There are some additional specifics in the book, but hopefully that's enough to give you a nice picture.
Past the canon, there is also some fan-created content related to Edens out there. Pretty much all of the good stuff is from the Fabula Rasa game, which features her as a prominent character: