Grieve was a prospect who won the 1998 American League Rookie of the Year award while playing for the Athletics.

[4] Grieve was selected by the Oakland Athletics with the second pick of the 1994 Major League Baseball draft, behind Paul Wilson.

[6] With the Devil Rays in 2001, he hit 11 HR with 72 RBI, Grieve's slugging percentage dropping a full 100 points from the prior year.

The following season (2002) he battled injuries, but did manage to hit 19 home runs and drive in 64 RBI in 136 games.

Grieve departed the Cubs in the 2004–2005 offseason as a free agent; he eventually signed with the Pittsburgh Pirates as a non-roster invitee to 2005 spring training.

He started the 2007 season still in the White Sox minor-league organization, a member of the AAA Charlotte Knights.