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No. Counterexamples were first constructed by Winkelmann, as quotients of A^5 $\mathbb A^5$ by algebraic actions of G_a$\mathbb G_{\text{a}}$. I learned this from Hanspeter Kraft's very nice article available here:
Recently Aravind Asok and Brent Doran have been studying these kinds of examples in the setting of A^1-homotopy $\mathbb A^1$-homotopy theory, on the arxiv as math/0703137.