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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.numdam.org/numdam-bin/item?id=SB_1994-1995__37__295_0.

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.

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:

Challenging problems on affine $n$-space.

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 On unipotent quotients and some A^1-contractible smooth schemes.

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.

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.numdam.org/numdam-bin/item?id=SB_1994-1995__37__295_0.

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.

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.

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.