Chan steps down on June 30 after a decade in which new epidemics such as bird flu and Ebola and decades-old campaigns against malaria, AIDS and malnutrition highlighted the complex health burden shouldered by the WHO.
Among the three vying to be the next WHO director-general is Ethiopia's former foreign and health minister, Tedros Adhanom, who if he wins would be the first African to hold the post.
Another former health minister, Sania Nishtar of Pakistan, is also on the list, as is WHO insider David Nabarro, a respected British doctor and diplomat who has spent two decades inside the UN system.
They are bidding to head perhaps the most influential of the United Nations agencies, which is responsible for coordinating the global response to health emergencies and raising awareness of health challenges ranging from pollution to obesity.
Tuesday marks the first time member states will actually get to choose between several finalists.
In the past, the executive committee presented them with a single candidate to accept and applaud.