Actually, NorthernDog, the Vice President is chosen by the Senate, not the House - see
U.S. Constitution Amendment XIIIn 1824, the VP was not decided by the Senate, as John Calhoun received 182 Electoral Votes vs. 78 Electoral Votes for all other VP candidates.
The Senate, however, did choose the VP in 1836 when the democratic electoral votes for Vice President were split between Richard Johnson (147) and William Smith (23) (with 124 Electoral Votes for other Vice Presidential candidates). Johnson won the Senate vote.
I'm actually not clear on whether the Senate actually voted for Burr in 1800, as the rules under Article II, Section 1 were in effect at the time state:
In every Case, after the Choice of the President, the Person having the greatest Number of Votes of the Electors shall be the Vice President. - which would have been Burr, without a Senate vote.
Dave
