The result of the private members' bill draw puts Mr Bryant in pole position as his proposal will get the most Parliamentary time allocated for debate.
A total of 20 MPs' names were drawn with the order determining which ones will get the most debating time.
His fellow Labour MPs, Steve Reed and Afzal Khan, came second and third.
A total of 461 MPs entered the ballot, which was drawn by a Commons clerk and announced by Deputy Speaker Lindsay Hoyle.
Private members' bills are one of the few chances MPs who are not ministers get to create legislation, although most are still likely to fall short.
This is because the lack of Parliamentary time allocated to them means they are not able to complete the legislative process.
Those that come high up in the ballot get the choice of time slots and thus stand a better chance.
Six bills from last year's ballot ended up becoming law, in areas including preventing violence against women, homelessness and parking.
Speaker John Bercow said: "Success in the private members' ballot allows backbench MPs a real opportunity to affect legislative change or, at the very least, bring to public attention an issue upon which they feel passionate."
Here's the full list of the 20 MPs whose names were drawn:
1.       Chris Bryant (Lab, Rhondda)
2.       Steve Reed (Lab, Croydon North)
3.       Afzal Khan (Lab, Manchester Gorton)
4.       Karen Buck (Labour, Westminster North)
5.       Tim Loughton (Con, East Worthing & Shoreham)
6.       Geoffrey Robinson (Lab, Coventry North West)
7.       Angus Brendan MacNeil (SNP, Na h-Eileanan an Iar)
8.       Kevin Hollinrake (Con, Thirsk & Malton)
9.       Jim McMahon (Lab Co-op, Oldham West & Royton)
10.   Glyn Davies (Con, Montgomeryshire)
11.   Sir Greg Knight (Con, East Yorkshire)
12.   Stuart Malcolm McDonald (SNP, Glasgow South)
13.   Esther McVey (Con, Tatton)
14.   Dr Sarah Wollaston (Con, Totnes)
15.   Stephanie Peacock (Lab, Barnsley East)
16.   Daniel Zeichner (Lab, Cambridge)
17.   Andy Slaughter (Lab, Hammersmith)
18.   Peter Kyle (Lab, Hove)
19.   Anne Marie Morris (Con, Newton Abbot)
20.   Holly Lynch (Lab, Halifax)
Labour MP Chris Bryant has won the annual ballot to decide which backbenchers get to propose new laws.