This is not possible now, but there is a work around. You can engage with the user in the public realm and ask them to send you private messages, but you can t send private messages back, only public ones. Of course, this all depends on if the user gives you the correct permissions.
If you have given permission to access a person s friends, you can then theoretically post on that users wall with references to each one of the friends, asking them to publicly interact with you and then potentially privately message you.
Get Friends
#if authenticated
https://graph.facebook.com/me/friends
http://developers.facebook.com/docs/reference/api/user/
Post in the Public Domain
http://developers.facebook.com/docs/reference/api/status/
Get Messages sent to that user (if given permission)
http://developers.facebook.com/docs/reference/api/message/