Coming at this with the perspective of looking for new team members, I really like the idea. My gut feeling is that it's going to give me a better impression of the person than a traditional CV/resume does.
Echoing concerns from some of the comments, however, as a developer I want to reuse my existing content from elsewhere in the Stack Exchange universe, so I'd like to see the story and a combination of additional information and curated stuff from elsewhere on Stack Exchange (including from my jobs profile). And why limit it to just Stack Overflow? My questions and answers on Home Improvement can give insight into how I approach problem solving, while other sites like Ask Different, Drupal AnswersDrupal Answers, etc. are more directly related to coding. I don't want to have to duplicate information because maintaining it becomes a nightmare. Just look at any online discussion of commenting code for an illustration of the issues that can come up.