Mikhail Gorbachev? Not a Jew; although the amount of scapegoating he's taken from Russians over the years, we can make him an honorary member. Leonid Brezhnev? Definitely not a Jew (although incorrectly rumored to be married to one). But the man between them (and we will conveniently forget the useless Konstantin Chernenko, the William Henry Harrison of Soviet leaders), Yuri Andropov... is it possible?
As it turns out, no. There are rumors circulating that Andropov's parents were both Jewish, but that is not the case. Andropov's father came from Cossack nobility. Andropov's mother was Finnish-German. Yes, her maiden name of Fleckenstein might have set off some alarms, but those look to be false. Germans are allowed to be Steins too.
And considering that prior to becoming the Soviet Premier, Andropov spent 15 years as the head of the KGB... We have no problems with counting him out.