No.  Counterexamples were first constructed by Winkelmann, as quotients of $\mathbb A^5$ by algebraic actions of $\mathbb G_{\text{a}}$.  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 $\mathbb A^1$-homotopy theory, on the arxiv as [math/0703137](http://arxiv.org/abs/math/0703137).