Well, before the Twelfth Amendement in 1804, it would have been very easily possible. Pre-12th Amendement, whoever received the most electoral votes became President, and second-most became Vice President. So if the election of 1800 is much less disputed (say Hamilton doesn't act like an ass), than no one will see any need for the Twelfth Amendment. Without the Twelfth Amendment, the following scenario is possible:
President Blankety-Blank is elected. Blankety-Blank serves four years. He then runs for re-election, but comes in second in electoral votes to Whatchamacallit. Seeing that he can remain in the spotlight for four years and then run again against Whatchamacallit, Blankety-Blank decides to accept the Vice Presidency.