No.  Counterexamples were first constructed by Winkelmann, as quotients of A^5 by algebraic actions of G_a.  I learned this from Hanspeter Kraft's very nice article available here: 

http://www.math.unibas.ch/~kraft/Papers/Bourbaki.pdf.

Recently Aravind Asok and Brent Doran have been studying these kinds of examples in the setting of A^1-homotopy theory, on the arxiv as math/0703137.