The foundation overseeing the development of Barack Obama’s presidential library began a global competition on Wednesday to select the architect who will design the elaborate Chicago complex.

The start of the selection process is the latest step in Mr. Obama’s quiet but painstaking planning for his post-presidential initiatives, which his advisers say could cost as much as $1 billion.

The library, to be located on the South Side of Chicago, where the president had his political start as a community organizer, will be the crown jewel of the effort, a high-technology take on the traditional archival presidential library that will include space for innovation labs, a community garden and sports.