Labour MP John McDonnell has defied odds estimated at 58,000 to 1 to top the annual Private Member's Bill ballot for two years in a row.
MPs' names are selected at random, with 240 having entered the draw this year.
The bills are a way for MPs to propose legislation on a subject of their choice. Those near the top of the list get Commons debating time, although they only rarely make it to law.
Mr McDonnell's bill would require MPs to approve Bank of England governors.
Speaking to the BBC's Mark D'Arcy the backbencher said it was "parliamentary history" and he was "absolutely staggered" to come first again.
"I wish I had thought of popping down to the bookmakers yesterday to be quite honest because we could have made a fortune," he added.
Traditionally MPs at the top of the list are lobbied hard by people who want specific issues to be chosen, with many not deciding - or announcing - their proposed topic for a few days.
But Mr McDonnell has already announced he intends to use his prime position on the list to bring in a bill requiring parliamentary approval for new Bank of England governors.
He said: "Under the Government's new legislation, the governor of the Bank of England will gain a vast range of new powers, more than any governor in our history.
"Therefore there should be a decisive, democratic input into the appointment of the new governor.
"Making the appointment subject to parliamentary approval will ensure this significant decision is not just left in the hands of the Chancellor and the person appointed will demonstrably have the confidence of Parliament."
Parliamentary clerks will need to approve the plan before the bill can be brought forward.
As first on the list, Mr McDonnell's bill is guaranteed debating time in the Commons although there is little chance of it, or any other, Private Member's Bill becoming law without the government throwing its weight behind it.
But bills can prove a good way of highlighting a subject in Parliament.
Barbara Keeley, who came third on the list, says she is considering introducing a bill which would place a duty on GPs and teachers to refer carers to sources of help and support.
Although not certain, Liberal Democrat John Hemming, placed sixth on the list, is thinking of proposing a change to the rules on secrecy in the courts, particularly the family courts.
Some private members' bills have brought about significant changes to the law, such as the Murder (Abolition of the Death Penalty) Act 1965, and the Abortion Act 1967.
'Giant gold coin'
In 2009, the now Welsh Secretary Cheryl Gillan was successful with her bill to improve the way local authorities provide support for people with autism.
The following year, under-18s were banned from using tanning salons thanks to Cardiff North MP Julie Morgan's bill.
In the 2010-12 session of parliament 7 Private Member's Bills became law.
One, the Coinage (Measurement) Act 2011, allows the Royal Mint to strike a 22-carat gold, one kilogram coin to commemorate the 2012 London Olympics. Before that, producing coins outside regulation weights was illegal.
From the 20 MPs drawn in the ballot more than half are Conservatives.
The party has 11 MPs on the list and Labour has six. The Liberal Democrats have two slots and the SNP has one.
The 20 MPs selected, in order, are:
Sir Paul Beresford