BERLIN (Reuters) - The far-right Alternative for Germany (AfD) beat Chancellor Angela Merkel's conservatives into third place in Sunday's regional election in the eastern state of Thuringia, in which the incumbent far-left Linke came first, an exit poll showed.

The result follows the AfD's successes in the eastern states of Saxony and Brandenburg, where it surged into second place in Sept. 1 elections, and marks a setback from Merkel's Christian Democrats (CDU).

The Linke, which heads the ruling state coalition with the SPD and Greens, won 29.5% of the vote, the exit poll for broadcaster ARD showed. The AfD won 24%, the CDU 22.5%, the Social Democrats 8.5%, the Greens 5.5% and the Free Democrats 5.0%. The result will make coalition building tricky.

(Reporting by Tassilo Hummel; Writing by Paul Carrel; Editing by Douglas Busvine)

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