Britton was born in Waco, Texas on May 22, 1989 and attended Tomball High School. The lefty was drafted out of Tomball in the 23rd round of the 2007 MLB Draft by the Boston Red Sox. Britton signed a $700,000 signing bonus with the Red Sox. He began his professional career in 2008 with the Class A shortseason Lowell Spinners, appearing in 8 games, 7 starts, with an ERA of 4.28 in 33.2 innings. In 2009, Britton split time between the Gulf Coast League Red Sox and Lowell; he combined to appear in 11.2 innings over 7 games. He missed most of the season due to Tommy John Surgery. 2010 saw Britton promotion to Class A fullseason Greenville Drive, where he started 21 games and earned a 2.97 ERA. Britton was promoted once again in 2011 to the Salem Red Sox. In Salem, Britton finished the season with 13 losses, a league worst. His 6.91 ERA was worst of all Carolina League starters.