Last astonishing Scottish Poll

STV report an incredible set of figures in the last pre-election poll:

“The poll, conducted for STV News and likely to be the last before polling day, shows the Nationalists gaining enough of the vote for 61 seats, 14 more than they had in the last parliamentary session.
Meanwhile, the poll indicates a major slump in support for Scottish Labour, with Iain Gray’s party taking a total of 33 seats.”

Can this type of outcome really happen? (The poll asked 1063 people – which is quite enough statistically…)