I haven't bought either of Obama's books, but I was browsing through the first one in a bookstore a few weeks ago, and read the passage where he described how he wound up going from Columbia to Chicago. As he told it, some guy in New York was looking for someone to be a community organizer in Chicago and recruited him for the job. I don't think it was Frank Davis.
At least that's how Obama told the story.
I can tell you how Obama got to Chicago. He was hired as a trainer by the Gemaliel Foundation, a group that trains community activist groups in Saul Alinsky organizing techniqes. Gemaliel sent him to Chicago.