This has just been on Radio 2, with the photographer and a representative from Wiki, plus other 'experts' commenting.
It seems to hinge on the exact circumstances of the shot, and there are conflicting stories ranging from total accident (nobody's copyright) to a complete set up (photographer's copyright). Speaking live, the photographer said he'd noticed the monkeys messing with his equipment and thought they might respond, so he put the camera on a tripod with wide-angle, set exposure, AF to servo, and left the remote release for them to play with. In other words, he set it all up, waited and watched and encouraged the monkeys take the shots.
Morally I think the copyright is the photographer's, and if it went to court, legally too.