With the resignation of Ashok Chavan as Maharashtra Chief Minister, time to pull out this old chestnut. Believe it or not, thanks to changing political fortunes, corruption, death, and elections, only one Maharashtra CM has ever completed a full 5-year term. Incidentally, his nephew was once a Maharashtra CM.
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Vasantrao Naik, from 1967 to 1972. In all, he enjoyed an unbroken stint as CM from Dec 1963 to Feb 1975 (three separate terms), also making him the state's longest-serving CM.