Allen Iverson and Kevin Garnett had been leading contenders to pull it off. If Garnett really does get traded--as seems increasingly likely--you'd have to put your money on Kobe Bryant, Dirk Nowitzki, and Dwyane Wade as most likely.
The Painted Area has a list of the ten players who have been in one place the longest. Plenty of surprises here, including Zydrunas Ilgauskas, Adonal Foyle, Jeff Foster, and three players straight from high school.
UPDATE: As a commenter rightly points out, I'm a total idiot. Of course Tim Duncan tops the list of most likely to spend an entire career in one uniform.