This is an interesting one, as I think there's really only three choices you can put here.
OF-Luis Gonzalez (1999-2006)
SP-Randy Johnson (1999-2004, 2007-?)
SP-Brandon Webb (2003-2006)
I can see a vote for Gonzalez, their longest tenured player, and who had that awesome and memorable 2001, his best season, and capped it off with the winning hit in the World Series.
Then there's Johnson, who had arguably the best 4 year peak ever, all for the D-Backs, and he's there right now and will probably win his 300th game as a D-Back if he stays healthy.
And Brandon Webb. He's been a pretty good pitcher, just won a Cy Young, and is the young leader on a young franchise.