The last, prior to Antonin Scalia, who died at some point Friday night or Saturday morning, was Chief Justice William Rehnquist, who died in 2005. Prior to that, the last justice to die while on the bench was Fred Vinson, who died in 1953 -- also while chief justice.
Which is another reason that the death of Scalia has disrupted business-as-usual in Washington. Usually, Capitol Hill can see a Supreme Court vacancy coming. Sometimes -- on more and more rare occasions -- it's out of everyone's control.