Beliveau, a graduate of Florida Atlantic University, was drafted in the 18th round of the 2008 draft by the Cubs. The pitcher appeared in 35 1/3 innings in 2008 with 52 strikeouts and a 2.80 ERA, before moving to Class-A in 2009 and then Class-A Advanced in 2010.
Opening the 2011 season wth Dayton of Class-A Advanced, Beliveau was promoted to Tennesse of Double-A ball. After being added to the 40-man roster in 2011, Beliveau pitched 17.2 innings with the Cubs with a 1-0 record and a 4.58 ERA. The native Providence, Rhode Island played for the US national baseball team in the 2011 Baseball World Cup, as well as the 2011 Pan American Games.
Beliveau has been ranked as the top left-handed prospect in the Cubs organization, touted for his ability to get outs without overpowering stuff.