And the composer is...

The legendary David Shire. From the story:

Shire to score Fincher's 'Zodiac'

Composer agency Evolution Music Partners has announced that veteran composer David Shire has been hired to compose the music for David Fincher’s new thriller, Zodiac. The film is based on Robert Graysmith’s books about the real life serial killer Zodiac who committed a number of murders in San Francisco during the 1960s and 1970s. The cast includes Jake Gyllenhaal, Robert Downey Jr, Mark Ruffalo, Anthony Edwards, Brian Cox and Dermot Mulroney. It’s scheduled to be released by Paramount Pictures on January 19.

Fittingly, 69-year old David Shire was one of the most prolific and hailed film composers in the 1970s. Among his best known credits from that era are The Conversation, All the President’s Men and The Taking of Pelham 1-2-3. His other credits include 2010, Return to Oz, Monkey Shines, The Hindenburg and Short Circuit.

Great news - thanks to Tibor Kapy for the heads up.