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Just call him Alex , its much easier .
Here's the answer from Wikipedia: pronounced [ɐlʲɪkˈsandr ɐlʲɪkˈsandrəvʲɪtɕ ɐˈlʲexʲɪn
Seriously though, here is an audio recording of Alekhine doing an interview. It was done in 1938 with the BBC.