He was born in Mesa, Arizona and attended Mount View High School there, excelling in both baseball, as a shortstop, and soccer. He attended Mesa Community college between 1994 and 1996, before being drafted by the Boston Red Sox in the 10th round of the 1996 amateur draft.
Hillenbrand played 72 games in 1996 for the low-A Lowell Spinners in the New York Penn. League. In 1997 he was promoted to the Sarasota Red Sox of the Florida State League, and was promoted again after 57 games, finishing the season with 64 games with the Michigan Battle Cats of the Midwestern League. Despite being drafted as a shortstop, he played at first base and third base his first two years in the minors.
In 1998, still with Michigan, he was converted to play catcher and responded with his best season in the minors, with a .349 batting average and 19 homeruns. This earned him a promotion in 1999 to AA Trenton Thunder of the Eastern League. However, a leg injury restricted him to only 69 games.
2000 saw Hillenbrand back at Trenton, now back to playing first base and third base as the injury prevented him from catching. An average season at age 25 did not bode well for his chances as a prospect, but he parlayed an invitation to spring training with the Red Sox in 2001 into a spot on the big-league team for opening day.
2001 saw him playing 139 games for the Sox, mostly at third base, but a .263 batting average failed to hide his failure to get on base adequately, nor to hit with power. However, he retained his spot on the roster for 2002, and responded with a much better season, with a .330 on-base percentage, and 20 home-runs contributing to a .459 slugging average. His play earned him the starting third baseman spot in the 2002 All Star Game.
Nevertheless, Hillenbrand entered the 2003 season the subject of trade rumors. The Red Sox had signed another third baseman, Bill Mueller, as a free-agent, and many believed that Hillenbrand's lack of strikezone judgment would not be compatible with the on-base percentage priorities of new Sox general manager Theo Epstein. Hillenbrand played 49 games with the Sox to start the 2003 season, but the career year of Bill Mueller had made Hillenbrand even more of a trading chip, and on May 29th, he was traded to the Arizona Diamondbacks for pitcher Byung-Hyun Kim.